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@article{DBLP:journals/jgo/SunHT24,
  author       = {Xiang{-}Kai Sun and
                  Jiayi Huang and
                  Kok Lay Teo},
  title        = {On semidefinite programming relaxations for a class of robust SOS-convex
                  polynomial optimization problems},
  journal      = {J. Glob. Optim.},
  volume       = {88},
  number       = {3},
  pages        = {755--776},
  year         = {2024}
}
@article{DBLP:journals/jgo/XuLDL23,
  author       = {Yingzhe Xu and
                  Cheng Lu and
                  Zhibin Deng and
                  Ya{-}Feng Liu},
  title        = {New semidefinite relaxations for a class of complex quadratic programming
                  problems},
  journal      = {J. Glob. Optim.},
  volume       = {87},
  number       = {1},
  pages        = {255--275},
  year         = {2023}
}
@article{DBLP:journals/corr/abs-2311-00882,
  author       = {Lorenzo Ciardo and
                  Stanislav Zivn{\'{y}}},
  title        = {Semidefinite programming and linear equations vs. homomorphism problems},
  journal      = {CoRR},
  volume       = {abs/2311.00882},
  year         = {2023}
}
@article{DBLP:journals/mor/GutekunstW22,
  author       = {Samuel C. Gutekunst and
                  David P. Williamson},
  title        = {Semidefinite Programming Relaxations of the Traveling Salesman Problem
                  and Their Integrality Gaps},
  journal      = {Math. Oper. Res.},
  volume       = {47},
  number       = {1},
  pages        = {1--28},
  year         = {2022}
}
@article{DBLP:journals/ol/Harrach22,
  author       = {Bastian Harrach},
  title        = {Solving an inverse elliptic coefficient problem by convex non-linear
                  semidefinite programming},
  journal      = {Optim. Lett.},
  volume       = {16},
  number       = {5},
  pages        = {1599--1609},
  year         = {2022}
}
@article{DBLP:journals/jscic/BellaviaGP21,
  author       = {Stefania Bellavia and
                  Jacek Gondzio and
                  Margherita Porcelli},
  title        = {A Relaxed Interior Point Method for Low-Rank Semidefinite Programming
                  Problems with Applications to Matrix Completion},
  journal      = {J. Sci. Comput.},
  volume       = {89},
  number       = {2},
  pages        = {46},
  year         = {2021}
}
@article{DBLP:journals/siamjo/DostertLM21,
  author       = {Maria Dostert and
                  David de Laat and
                  Philippe Moustrou},
  title        = {Exact Semidefinite Programming Bounds for Packing Problems},
  journal      = {{SIAM} J. Optim.},
  volume       = {31},
  number       = {2},
  pages        = {1433--1458},
  year         = {2021}
}
@article{DBLP:journals/corr/abs-2105-11440,
  author       = {Bastian Harrach},
  title        = {Solving an inverse elliptic coefficient problem by convex non-linear
                  semidefinite programming},
  journal      = {CoRR},
  volume       = {abs/2105.11440},
  year         = {2021}
}
@article{DBLP:journals/cam/BirginGHMS20,
  author       = {Ernesto G. Birgin and
                  Walter G{\'{o}}mez and
                  Gabriel Haeser and
                  Leonardo M. Mito and
                  Daiana O. Santos},
  title        = {An Augmented Lagrangian algorithm for nonlinear semidefinite programming
                  applied to the covering problem},
  journal      = {Comput. Appl. Math.},
  volume       = {39},
  number       = {1},
  year         = {2020}
}
@article{DBLP:journals/eor/GuimaraesCP20,
  author       = {Dilson Almeida Guimar{\~{a}}es and
                  Alexandre Salles da Cunha and
                  Dilson Lucas Pereira},
  title        = {Semidefinite programming lower bounds and branch-and-bound algorithms
                  for the quadratic minimum spanning tree problem},
  journal      = {Eur. J. Oper. Res.},
  volume       = {280},
  number       = {1},
  pages        = {46--58},
  year         = {2020}
}
@article{DBLP:journals/jcam/LiZZ20,
  author       = {Lidan Li and
                  Liwei Zhang and
                  Hongwei Zhang},
  title        = {Inverse semidefinite quadratic programming problem with l1 norm measure},
  journal      = {J. Comput. Appl. Math.},
  volume       = {376},
  pages        = {112838},
  year         = {2020}
}
@article{DBLP:journals/corr/abs-2012-10046,
  author       = {Yian Chen and
                  Yuehaw Khoo and
                  Michael Lindsey},
  title        = {Multiscale semidefinite programming approach to positioning problems
                  with pairwise structure},
  journal      = {CoRR},
  volume       = {abs/2012.10046},
  year         = {2020}
}
@article{DBLP:journals/jcam/NiksereshtN19,
  author       = {Asiye Nikseresht and
                  Alireza Nazemi},
  title        = {A novel neural network for solving semidefinite programming problems
                  with some applications},
  journal      = {J. Comput. Appl. Math.},
  volume       = {350},
  pages        = {309--323},
  year         = {2019}
}
@article{DBLP:journals/ol/XuTL19,
  author       = {Zi Xu and
                  Siqi Tao and
                  Kaiyao Lou},
  title        = {Semidefinite approximation bound for a class of nonhomogeneous nonconvex
                  quadratically constrained quadratic programming problem},
  journal      = {Optim. Lett.},
  volume       = {13},
  number       = {4},
  pages        = {837--845},
  year         = {2019}
}
@inproceedings{DBLP:conf/aaai/WangK19,
  author       = {Po{-}Wei Wang and
                  J. Zico Kolter},
  title        = {Low-Rank Semidefinite Programming for the {MAX2SAT} Problem},
  booktitle    = {{AAAI}},
  pages        = {1641--1649},
  publisher    = {{AAAI} Press},
  year         = {2019}
}
@inproceedings{DBLP:conf/cdc/DavoudiHR19,
  author       = {Ramtin Davoudi and
                  Seyed Mohammad Hosseini and
                  Amin Ramezani},
  title        = {A semidefinite programming approach for stochastic switched optimal
                  control problems},
  booktitle    = {{CDC}},
  pages        = {2503--2508},
  publisher    = {{IEEE}},
  year         = {2019}
}
@inproceedings{DBLP:conf/codit/ElloumiLL19,
  author       = {Sourour Elloumi and
                  Am{\'{e}}lie Lambert and
                  Arnaud Lazare},
  title        = {Semidefinite programming relaxations through quadratic reformulation
                  for box-constrained polynomial optimization problems},
  booktitle    = {CoDIT},
  pages        = {1498--1503},
  publisher    = {{IEEE}},
  year         = {2019}
}
@article{DBLP:journals/corr/abs-1907-09054,
  author       = {Samuel C. Gutekunst and
                  David P. Williamson},
  title        = {Semidefinite Programming Relaxations of the Traveling Salesman Problem
                  and Their Integrality Gaps},
  journal      = {CoRR},
  volume       = {abs/1907.09054},
  year         = {2019}
}
@article{DBLP:journals/corr/abs-1908-06320,
  author       = {Giannis Nikolentzos and
                  Michalis Vazirgiannis},
  title        = {Revisiting the Graph Isomorphism Problem with Semidefinite Programming},
  journal      = {CoRR},
  volume       = {abs/1908.06320},
  year         = {2019}
}
@article{DBLP:journals/corr/abs-1909-06099,
  author       = {Stefania Bellavia and
                  Jacek Gondzio and
                  Margherita Porcelli},
  title        = {A relaxed interior point method for low-rank semidefinite programming
                  problems},
  journal      = {CoRR},
  volume       = {abs/1909.06099},
  year         = {2019}
}
@article{DBLP:journals/coap/FerreiraKS18,
  author       = {Jos{\'{e}} F. S. Bravo Ferreira and
                  Yuehaw Khoo and
                  Amit Singer},
  title        = {Semidefinite programming approach for the quadratic assignment problem
                  with a sparse graph},
  journal      = {Comput. Optim. Appl.},
  volume       = {69},
  number       = {3},
  pages        = {677--712},
  year         = {2018}
}
@article{DBLP:journals/jcam/NiksereshtN18,
  author       = {Asiye Nikseresht and
                  Alireza Nazemi},
  title        = {A novel neural network model for solving a class of nonlinear semidefinite
                  programming problems},
  journal      = {J. Comput. Appl. Math.},
  volume       = {338},
  pages        = {69--79},
  year         = {2018}
}
@inproceedings{DBLP:conf/amcc/YuanL18,
  author       = {Jianjun Yuan and
                  Andrew G. Lamperski},
  title        = {A Random Algorithm for Semidefinite Programming Problems},
  booktitle    = {{ACC}},
  pages        = {1382--1387},
  publisher    = {{IEEE}},
  year         = {2018}
}
@article{DBLP:journals/corr/abs-1812-06362,
  author       = {Po{-}Wei Wang and
                  J. Zico Kolter},
  title        = {Low-rank semidefinite programming for the {MAX2SAT} problem},
  journal      = {CoRR},
  volume       = {abs/1812.06362},
  year         = {2018}
}
@article{DBLP:journals/dam/Hungerlander17,
  author       = {Philipp Hungerl{\"{a}}nder},
  title        = {New semidefinite programming relaxations for the Linear Ordering and
                  the Traveling Salesman Problem},
  journal      = {Discret. Appl. Math.},
  volume       = {217},
  pages        = {19--39},
  year         = {2017}
}
@article{DBLP:journals/disopt/LeeM17,
  author       = {Timothy Lee and
                  John E. Mitchell},
  title        = {Approximation algorithms from inexact solutions to semidefinite programming
                  relaxations of combinatorial optimization problems},
  journal      = {Discret. Optim.},
  volume       = {24},
  pages        = {152--169},
  year         = {2017}
}
@article{DBLP:journals/jco/GarraffaCS17,
  author       = {Michele Garraffa and
                  Federico Della Croce and
                  Fabio Salassa},
  title        = {An exact semidefinite programming approach for the max-mean dispersion
                  problem},
  journal      = {J. Comb. Optim.},
  volume       = {34},
  number       = {1},
  pages        = {71--93},
  year         = {2017}
}
@article{DBLP:journals/mp/SudaTT17,
  author       = {Sho Suda and
                  Hajime Tanaka and
                  Norihide Tokushige},
  title        = {A semidefinite programming approach to a cross-intersection problem
                  with measures},
  journal      = {Math. Program.},
  volume       = {166},
  number       = {1-2},
  pages        = {113--130},
  year         = {2017}
}
@article{DBLP:journals/siamjo/SakaueTKI17,
  author       = {Shinsaku Sakaue and
                  Akiko Takeda and
                  Sunyoung Kim and
                  Naoki Ito},
  title        = {Exact Semidefinite Programming Relaxations with Truncated Moment Matrix
                  for Binary Polynomial Optimization Problems},
  journal      = {{SIAM} J. Optim.},
  volume       = {27},
  number       = {1},
  pages        = {565--582},
  year         = {2017}
}
@article{DBLP:journals/apjor/WuZZL16,
  author       = {Jia Wu and
                  Yi Zhang and
                  Liwei Zhang and
                  Yue Lu},
  title        = {A Sequential Convex Program Approach to an Inverse Linear Semidefinite
                  Programming Problem},
  journal      = {Asia Pac. J. Oper. Res.},
  volume       = {33},
  number       = {4},
  pages        = {1650025:1--1650025:26},
  year         = {2016}
}
@article{DBLP:journals/coap/PongSWW16,
  author       = {Ting Kei Pong and
                  Hao Sun and
                  Ningchuan Wang and
                  Henry Wolkowicz},
  title        = {Eigenvalue, quadratic programming, and semidefinite programming relaxations
                  for a cut minimization problem},
  journal      = {Comput. Optim. Appl.},
  volume       = {63},
  number       = {2},
  pages        = {333--364},
  year         = {2016}
}
@article{DBLP:journals/jco/WuXDX16,
  author       = {Chenchen Wu and
                  Dachuan Xu and
                  Donglei Du and
                  Wen{-}qing Xu},
  title        = {An approximation algorithm for the balanced Max-3-Uncut problem using
                  complex semidefinite programming rounding},
  journal      = {J. Comb. Optim.},
  volume       = {32},
  number       = {4},
  pages        = {1017--1035},
  year         = {2016}
}
@article{DBLP:journals/jgo/JeyakumarKLL16,
  author       = {Vaithilingam Jeyakumar and
                  S. Kim and
                  Gue Myung Lee and
                  Guoyin Li},
  title        = {Semidefinite programming relaxation methods for global optimization
                  problems with sparse polynomials and unbounded semialgebraic feasible
                  sets},
  journal      = {J. Glob. Optim.},
  volume       = {65},
  number       = {2},
  pages        = {175--190},
  year         = {2016}
}
@article{DBLP:journals/siamjo/JeyakumarLLP16,
  author       = {Vaithilingam Jeyakumar and
                  Jean B. Lasserre and
                  Guoyin Li and
                  T. S. Pham},
  title        = {Convergent Semidefinite Programming Relaxations for Global Bilevel
                  Polynomial Optimization Problems},
  journal      = {{SIAM} J. Optim.},
  volume       = {26},
  number       = {1},
  pages        = {753--780},
  year         = {2016}
}
@inproceedings{DBLP:conf/cdc/AshraphijuoFLA16,
  author       = {Morteza Ashraphijuo and
                  Salar Fattahi and
                  Javad Lavaei and
                  Alper Atamt{\"{u}}rk},
  title        = {A strong semidefinite programming relaxation of the unit commitment
                  problem},
  booktitle    = {{CDC}},
  pages        = {694--701},
  publisher    = {{IEEE}},
  year         = {2016}
}
@inproceedings{DBLP:conf/cpsweek/DrzajicKKL16,
  author       = {Dalibor Drzajic and
                  Nikolaos Kariotoglou and
                  Maryam Kamgarpour and
                  John Lygeros},
  title        = {A Semidefinite Programming Approach to Control Synthesis for Stochastic
                  Reach-Avoid Problems},
  booktitle    = {ARCH@CPSWeek},
  series       = {EPiC Series in Computing},
  volume       = {43},
  pages        = {134--143},
  publisher    = {EasyChair},
  year         = {2016}
}
@phdthesis{DBLP:phd/jp/Yamakawa15,
  author       = {Yuya Yamakawa},
  title        = {Studies on Optimization Methods for Nonlinear Semidefinite Programming
                  Problems},
  school       = {Kyoto University, Japan},
  year         = {2015}
}
@article{DBLP:journals/informs/KlerkST15,
  author       = {Etienne de Klerk and
                  Renata Sotirov and
                  Uwe Truetsch},
  title        = {A New Semidefinite Programming Relaxation for the Quadratic Assignment
                  Problem and Its Computational Perspectives},
  journal      = {{INFORMS} J. Comput.},
  volume       = {27},
  number       = {2},
  pages        = {378--391},
  year         = {2015}
}
@article{DBLP:journals/jco/WuDX15,
  author       = {Chenchen Wu and
                  Donglei Du and
                  Dachuan Xu},
  title        = {An improved semidefinite programming hierarchies rounding approximation
                  algorithm for maximum graph bisection problems},
  journal      = {J. Comb. Optim.},
  volume       = {29},
  number       = {1},
  pages        = {53--66},
  year         = {2015}
}
@article{DBLP:journals/mp/DamS15,
  author       = {Edwin R. van Dam and
                  Renata Sotirov},
  title        = {Semidefinite programming and eigenvalue bounds for the graph partition
                  problem},
  journal      = {Math. Program.},
  volume       = {151},
  number       = {2},
  pages        = {379--404},
  year         = {2015}
}
@article{DBLP:journals/mp/LaatV15,
  author       = {David de Laat and
                  Frank Vallentin},
  title        = {A semidefinite programming hierarchy for packing problems in discrete
                  geometry},
  journal      = {Math. Program.},
  volume       = {151},
  number       = {2},
  pages        = {529--553},
  year         = {2015}
}
@article{DBLP:journals/siamjo/Auslender15,
  author       = {Alfred Auslender},
  title        = {An Exact Penalty Method for Nonconvex Problems Covering, in Particular,
                  Nonlinear Programming, Semidefinite Programming, and Second-Order
                  Cone Programming},
  journal      = {{SIAM} J. Optim.},
  volume       = {25},
  number       = {3},
  pages        = {1732--1759},
  year         = {2015}
}
@article{DBLP:journals/toms/Wittek15,
  author       = {Peter Wittek},
  title        = {Algorithm 950: Ncpol2sdpa - Sparse Semidefinite Programming Relaxations
                  for Polynomial Optimization Problems of Noncommuting Variables},
  journal      = {{ACM} Trans. Math. Softw.},
  volume       = {41},
  number       = {3},
  pages        = {21:1--21:12},
  year         = {2015}
}
@inproceedings{DBLP:conf/cdc/MadaniKL15,
  author       = {Ramtin Madani and
                  Abdulrahman Kalbat and
                  Javad Lavaei},
  title        = {{ADMM} for sparse semidefinite programming with applications to optimal
                  power flow problem},
  booktitle    = {{CDC}},
  pages        = {5932--5939},
  publisher    = {{IEEE}},
  year         = {2015}
}
@article{DBLP:journals/coap/MonteiroOS14,
  author       = {Renato D. C. Monteiro and
                  Camilo Ortiz and
                  Benar Fux Svaiter},
  title        = {Implementation of a block-decomposition algorithm for solving large-scale
                  conic semidefinite programming problems},
  journal      = {Comput. Optim. Appl.},
  volume       = {57},
  number       = {1},
  pages        = {45--69},
  year         = {2014}
}
@article{DBLP:journals/eor/GicquelLM14,
  author       = {C{\'{e}}line Gicquel and
                  Abdel Lisser and
                  Michel Minoux},
  title        = {An evaluation of semidefinite programming based approaches for discrete
                  lot-sizing problems},
  journal      = {Eur. J. Oper. Res.},
  volume       = {237},
  number       = {2},
  pages        = {498--507},
  year         = {2014}
}
@article{DBLP:journals/informs/Sotirov14,
  author       = {Renata Sotirov},
  title        = {An Efficient Semidefinite Programming Relaxation for the Graph Partition
                  Problem},
  journal      = {{INFORMS} J. Comput.},
  volume       = {26},
  number       = {1},
  pages        = {16--30},
  year         = {2014}
}
@inproceedings{DBLP:conf/cocoon/WuXDX14,
  author       = {Chenchen Wu and
                  Dachuan Xu and
                  Donglei Du and
                  Wen{-}qing Xu},
  title        = {A Complex Semidefinite Programming Rounding Approximation Algorithm
                  for the Balanced Max-3-Uncut Problem},
  booktitle    = {{COCOON}},
  series       = {Lecture Notes in Computer Science},
  volume       = {8591},
  pages        = {324--335},
  publisher    = {Springer},
  year         = {2014}
}
@inproceedings{DBLP:conf/ipps/FujisawaEYSMMW14,
  author       = {Katsuki Fujisawa and
                  Toshio Endo and
                  Yuichiro Yasui and
                  Hitoshi Sato and
                  Naoki Matsuzawa and
                  Satoshi Matsuoka and
                  Hayato Waki},
  title        = {Petascale General Solver for Semidefinite Programming Problems with
                  Over Two Million Constraints},
  booktitle    = {{IPDPS}},
  pages        = {1171--1180},
  publisher    = {{IEEE} Computer Society},
  year         = {2014}
}
@article{DBLP:journals/cejor/GovorcinGP13,
  author       = {Jelena Govorcin and
                  Nebojsa Gvozdenovic and
                  Janez Povh},
  title        = {New heuristics for the vertex coloring problem based on semidefinite
                  programming},
  journal      = {Central Eur. J. Oper. Res.},
  volume       = {21},
  number       = {Supplement-1},
  pages        = {13--25},
  year         = {2013}
}
@inproceedings{DBLP:conf/cocoon/WuDX13,
  author       = {Chenchen Wu and
                  Donglei Du and
                  Dachuan Xu},
  title        = {An Improved Semidefinite Programming Hierarchies Rounding Approximation
                  Algorithm for Maximum Graph Bisection Problems},
  booktitle    = {{COCOON}},
  series       = {Lecture Notes in Computer Science},
  volume       = {7936},
  pages        = {304--315},
  publisher    = {Springer},
  year         = {2013}
}
@inproceedings{DBLP:conf/spawc/El-AbsiEK13,
  author       = {Mohammed El{-}Absi and
                  Mohamed El{-}Hadidy and
                  Thomas Kaiser},
  title        = {Min-maxing interference alignment algorithm as a semidefinite programming
                  problem},
  booktitle    = {{SPAWC}},
  pages        = {290--294},
  publisher    = {{IEEE}},
  year         = {2013}
}
@article{DBLP:journals/corr/Wittek13,
  author       = {Peter Wittek},
  title        = {Ncpol2sdpa - Sparse Semidefinite Programming Relaxations for Polynomial
                  Optimization Problems of Noncommuting Variables},
  journal      = {CoRR},
  volume       = {abs/1308.6029},
  year         = {2013}
}
@article{DBLP:journals/automatica/OishiA12,
  author       = {Yasuaki Oishi and
                  Teodoro Alamo},
  title        = {Robust semidefinite programming problems with general nonlinear parameter
                  dependence: Approaches using the DC-representations},
  journal      = {Autom.},
  volume       = {48},
  number       = {11},
  pages        = {2937--2944},
  year         = {2012}
}
@article{DBLP:journals/coap/SheraliDD12,
  author       = {Hanif D. Sherali and
                  Evrim Dalkiran and
                  Jitamitra Desai},
  title        = {Enhancing RLT-based relaxations for polynomial programming problems
                  via a new class of \emph{v}-semidefinite cuts},
  journal      = {Comput. Optim. Appl.},
  volume       = {52},
  number       = {2},
  pages        = {483--506},
  year         = {2012}
}
@article{DBLP:journals/coap/WakiNM12,
  author       = {Hayato Waki and
                  Maho Nakata and
                  Masakazu Muramatsu},
  title        = {Strange behaviors of interior-point methods for solving semidefinite
                  programming problems in polynomial optimization},
  journal      = {Comput. Optim. Appl.},
  volume       = {53},
  number       = {3},
  pages        = {823--844},
  year         = {2012}
}
@article{DBLP:journals/jgo/Tsuchiya12,
  author       = {Takeshi Tsuchiya},
  title        = {Global optimization of polynomial-expressed nonlinear optimal control
                  problems with semidefinite programming relaxation},
  journal      = {J. Glob. Optim.},
  volume       = {54},
  number       = {4},
  pages        = {831--854},
  year         = {2012}
}
@article{DBLP:journals/mp/KlerkS12,
  author       = {Etienne de Klerk and
                  Renata Sotirov},
  title        = {Improved semidefinite programming bounds for quadratic assignment
                  problems with suitable symmetry},
  journal      = {Math. Program.},
  volume       = {133},
  number       = {1-2},
  pages        = {75--91},
  year         = {2012}
}
@article{DBLP:journals/mp/LarakiL12,
  author       = {Rida Laraki and
                  Jean B. Lasserre},
  title        = {Semidefinite programming for min-max problems and games},
  journal      = {Math. Program.},
  volume       = {131},
  number       = {1-2},
  pages        = {305--332},
  year         = {2012}
}
@article{DBLP:journals/mp/MalickR12,
  author       = {J{\'{e}}r{\^{o}}me Malick and
                  Fr{\'{e}}d{\'{e}}ric Roupin},
  title        = {Solving k-cluster problems to optimality with semidefinite programming},
  journal      = {Math. Program.},
  volume       = {136},
  number       = {2},
  pages        = {279--300},
  year         = {2012}
}
@article{DBLP:journals/orl/BeckDT12,
  author       = {Amir Beck and
                  Yoel Drori and
                  Marc Teboulle},
  title        = {A new semidefinite programming relaxation scheme for a class of quadratic
                  matrix problems},
  journal      = {Oper. Res. Lett.},
  volume       = {40},
  number       = {4},
  pages        = {298--302},
  year         = {2012}
}
@article{DBLP:journals/orl/JeyakumarL12,
  author       = {Vaithilingam Jeyakumar and
                  Guoyin Li},
  title        = {Exact {SDP} relaxations for classes of nonlinear semidefinite programming
                  problems},
  journal      = {Oper. Res. Lett.},
  volume       = {40},
  number       = {6},
  pages        = {529--536},
  year         = {2012}
}
@article{DBLP:journals/toms/KimKWY12,
  author       = {Sunyoung Kim and
                  Masakazu Kojima and
                  Hayato Waki and
                  Makoto Yamashita},
  title        = {Algorithm 920: {SFSDP:} {A} Sparse Version of Full Semidefinite Programming
                  Relaxation for Sensor Network Localization Problems},
  journal      = {{ACM} Trans. Math. Softw.},
  volume       = {38},
  number       = {4},
  pages        = {27:1--27:19},
  year         = {2012}
}
@article{DBLP:journals/toms/YamashitaFFNN12,
  author       = {Makoto Yamashita and
                  Katsuki Fujisawa and
                  Mituhiro Fukuda and
                  Kazuhide Nakata and
                  Maho Nakata},
  title        = {Algorithm 925: Parallel Solver for Semidefinite Programming Problem
                  having Sparse Schur Complement Matrix},
  journal      = {{ACM} Trans. Math. Softw.},
  volume       = {39},
  number       = {1},
  pages        = {6:1--6:22},
  year         = {2012}
}
@article{DBLP:journals/wpc/MuZ12,
  author       = {Xuewen Mu and
                  Yaling Zhang},
  title        = {A New Rank-two Semidefinite Programming Relaxation Method for Multiuser
                  Detection Problem},
  journal      = {Wirel. Pers. Commun.},
  volume       = {65},
  number       = {1},
  pages        = {223--233},
  year         = {2012}
}
@inproceedings{DBLP:conf/sc/FujisawaSMEYN12,
  author       = {Katsuki Fujisawa and
                  Hitoshi Sato and
                  Satoshi Matsuoka and
                  Toshio Endo and
                  Makoto Yamashita and
                  Maho Nakata},
  title        = {High-performance general solver for extremely large-scale semidefinite
                  programming problems},
  booktitle    = {{SC}},
  pages        = {93},
  publisher    = {{IEEE/ACM}},
  year         = {2012}
}
@article{DBLP:journals/anor/GhaddarAL11,
  author       = {Bissan Ghaddar and
                  Miguel F. Anjos and
                  Frauke Liers},
  title        = {A branch-and-cut algorithm based on semidefinite programming for the
                  minimum \emph{k}-partition problem},
  journal      = {Ann. Oper. Res.},
  volume       = {188},
  number       = {1},
  pages        = {155--174},
  year         = {2011}
}
@article{DBLP:journals/rairo/MeiraM11,
  author       = {Luis A. A. Meira and
                  Fl{\'{a}}vio Keidi Miyazawa},
  title        = {Semidefinite Programming Based Algorithms for the Sparsest Cut Problem},
  journal      = {{RAIRO} Oper. Res.},
  volume       = {45},
  number       = {2},
  pages        = {75--100},
  year         = {2011}
}
@article{DBLP:journals/siamjo/KlerkL11,
  author       = {Etienne de Klerk and
                  Monique Laurent},
  title        = {On the Lasserre Hierarchy of Semidefinite Programming Relaxations
                  of Convex Polynomial Optimization Problems},
  journal      = {{SIAM} J. Optim.},
  volume       = {21},
  number       = {3},
  pages        = {824--832},
  year         = {2011}
}
@inproceedings{DBLP:conf/allerton/LesieutreMBD11,
  author       = {Bernard C. Lesieutre and
                  Daniel K. Molzahn and
                  Alexander R. Borden and
                  Christopher L. DeMarco},
  title        = {Examining the limits of the application of semidefinite programming
                  to power flow problems},
  booktitle    = {Allerton},
  pages        = {1492--1499},
  publisher    = {{IEEE}},
  year         = {2011}
}
@article{DBLP:journals/amcs/Muhafzan10,
  author       = {Muhafzan},
  title        = {Use of semidefinite programming for solving the {LQR} problem subject
                  to rectangular descriptor systems},
  journal      = {Int. J. Appl. Math. Comput. Sci.},
  volume       = {20},
  number       = {4},
  pages        = {655--664},
  year         = {2010}
}
@article{DBLP:journals/jgo/KimK10,
  author       = {Sunyoung Kim and
                  Masakazu Kojima},
  title        = {Solving polynomial least squares problems via semidefinite programming
                  relaxations},
  journal      = {J. Glob. Optim.},
  volume       = {46},
  number       = {1},
  pages        = {1--23},
  year         = {2010}
}
@article{DBLP:journals/mp/KlerkS10,
  author       = {Etienne de Klerk and
                  Renata Sotirov},
  title        = {Exploiting group symmetry in semidefinite programming relaxations
                  of the quadratic assignment problem},
  journal      = {Math. Program.},
  volume       = {122},
  number       = {2},
  pages        = {225--246},
  year         = {2010}
}
@article{DBLP:journals/siamjo/MittelmannP10,
  author       = {Hans D. Mittelmann and
                  Jiming Peng},
  title        = {Estimating Bounds for Quadratic Assignment Problems Associated with
                  Hamming and Manhattan Distance Matrices Based on Semidefinite Programming},
  journal      = {{SIAM} J. Optim.},
  volume       = {20},
  number       = {6},
  pages        = {3408--3426},
  year         = {2010}
}
@inproceedings{DBLP:conf/icms/Kojima10,
  author       = {Masakazu Kojima},
  title        = {Exploiting Structured Sparsity in Large Scale Semidefinite Programming
                  Problems},
  booktitle    = {{ICMS}},
  series       = {Lecture Notes in Computer Science},
  volume       = {6327},
  pages        = {4--9},
  publisher    = {Springer},
  year         = {2010}
}
@article{DBLP:journals/siamjo/KlerkPS09,
  author       = {Etienne de Klerk and
                  Dmitrii V. Pasechnik and
                  Renata Sotirov},
  title        = {Erratum: On Semidefinite Programming Relaxations of the Traveling
                  Salesman Problem},
  journal      = {{SIAM} J. Optim.},
  volume       = {20},
  number       = {2},
  pages        = {1132},
  year         = {2009}
}
@article{DBLP:journals/tac/Oishi09,
  author       = {Yasuaki Oishi},
  title        = {An Asymptotically Exact Approach to Robust Semidefinite Programming
                  Problems with Function Variables},
  journal      = {{IEEE} Trans. Autom. Control.},
  volume       = {54},
  number       = {5},
  pages        = {1000--1006},
  year         = {2009}
}
@incollection{DBLP:reference/opt/CommanderRY09,
  author       = {Clayton W. Commander and
                  Michelle A. Ragle and
                  Yinyu Ye},
  title        = {Semidefinite Programming and the Sensor Network Localization Problem,
                  {SNLP}},
  booktitle    = {Encyclopedia of Optimization},
  pages        = {3384--3390},
  publisher    = {Springer},
  year         = {2009}
}
@article{DBLP:journals/cejor/Al-Homidan08,
  author       = {Suliman Al{-}Homidan},
  title        = {Semidefinite programming for the educational testing problem},
  journal      = {Central Eur. J. Oper. Res.},
  volume       = {16},
  number       = {3},
  pages        = {239--249},
  year         = {2008}
}
@article{DBLP:journals/informs/AnjosV08,
  author       = {Miguel F. Anjos and
                  Anthony Vannelli},
  title        = {Computing Globally Optimal Solutions for Single-Row Layout Problems
                  Using Semidefinite Programming and Cutting Planes},
  journal      = {{INFORMS} J. Comput.},
  volume       = {20},
  number       = {4},
  pages        = {611--617},
  year         = {2008}
}
@article{DBLP:journals/mp/Lasserre08,
  author       = {Jean B. Lasserre},
  title        = {A semidefinite programming approach to the generalized problem of
                  moments},
  journal      = {Math. Program.},
  volume       = {112},
  number       = {1},
  pages        = {65--92},
  year         = {2008}
}
@article{DBLP:journals/siamjo/KlerkPS08,
  author       = {Etienne de Klerk and
                  Dmitrii V. Pasechnik and
                  Renata Sotirov},
  title        = {On Semidefinite Programming Relaxations of the Traveling Salesman
                  Problem},
  journal      = {{SIAM} J. Optim.},
  volume       = {19},
  number       = {4},
  pages        = {1559--1573},
  year         = {2008}
}
@article{DBLP:journals/toms/WakiKKMS08,
  author       = {Hayato Waki and
                  Sunyoung Kim and
                  Masakazu Kojima and
                  Masakazu Muramatsu and
                  Hiroshi Sugimoto},
  title        = {Algorithm 883: SparsePOP - {A} Sparse Semidefinite Programming Relaxation
                  of Polynomial Optimization Problems},
  journal      = {{ACM} Trans. Math. Softw.},
  volume       = {35},
  number       = {2},
  pages        = {15:1--15:13},
  year         = {2008}
}
@phdthesis{DBLP:phd/us/So07,
  author       = {Anthony Man{-}Cho So},
  title        = {A semidefinite programming approach to the graph realization problem
                  : theory, applications and extensions},
  school       = {Stanford University, {USA}},
  year         = {2007}
}
@article{DBLP:journals/mp/DukanovicR07,
  author       = {Igor Dukanovic and
                  Franz Rendl},
  title        = {Semidefinite programming relaxations for graph coloring and maximal
                  clique problems},
  journal      = {Math. Program.},
  volume       = {109},
  number       = {2-3},
  pages        = {345--365},
  year         = {2007}
}
@article{DBLP:journals/mp/SoZY07,
  author       = {Anthony Man{-}Cho So and
                  Jiawei Zhang and
                  Yinyu Ye},
  title        = {On approximating complex quadratic optimization problems via semidefinite
                  programming relaxations},
  journal      = {Math. Program.},
  volume       = {110},
  number       = {1},
  pages        = {93--110},
  year         = {2007}
}
@inproceedings{DBLP:conf/cvpr/OlssonEK07,
  author       = {Carl Olsson and
                  Anders P. Eriksson and
                  Fredrik Kahl},
  title        = {Solving Large Scale Binary Quadratic Problems: Spectral Methods vs.
                  Semidefinite Programming},
  booktitle    = {{CVPR}},
  publisher    = {{IEEE} Computer Society},
  year         = {2007}
}
@incollection{DBLP:reference/crc/ZhangYS07,
  author       = {Jiawei Zhang and
                  Yinyu Ye and
                  Anthony Man{-}Cho So},
  title        = {On Analyzing Semidefinite Programming Relaxations of Complex Quadratic
                  Optimization Problems},
  booktitle    = {Handbook of Approximation Algorithms and Metaheuristics},
  publisher    = {Chapman and Hall/CRC},
  year         = {2007}
}
@article{DBLP:journals/coap/KrishnanM06,
  author       = {Kartik Krishnan and
                  John E. Mitchell},
  title        = {A Semidefinite Programming Based Polyhedral Cut and Price Approach
                  for the Maxcut Problem},
  journal      = {Comput. Optim. Appl.},
  volume       = {33},
  number       = {1},
  pages        = {51--71},
  year         = {2006}
}
@article{DBLP:journals/cor/MiyashiroM06,
  author       = {Ryuhei Miyashiro and
                  Tomomi Matsui},
  title        = {Semidefinite programming based approaches to the break minimization
                  problem},
  journal      = {Comput. Oper. Res.},
  volume       = {33},
  pages        = {1975--1982},
  year         = {2006}
}
@article{DBLP:journals/mp/MalikJHG06,
  author       = {Umar Malik and
                  Imad M. Jaimoukha and
                  G. D. Halikias and
                  S. K. Gungah},
  title        = {On the gap between the quadratic integer programming problem and its
                  semidefinite relaxation},
  journal      = {Math. Program.},
  volume       = {107},
  number       = {3},
  pages        = {505--515},
  year         = {2006}
}
@inproceedings{DBLP:conf/dagstuhl/Barnum06,
  author       = {Howard Barnum},
  title        = {Semidefinite programming characterization and spectral adversary method
                  for quantum complexity with noncommuting unitary queries},
  booktitle    = {Algorithms and Complexity for Continuous Problems},
  series       = {Dagstuhl Seminar Proceedings},
  volume       = {06391},
  publisher    = {Internationales Begegnungs- und Forschungszentrum fuer Informatik
                  (IBFI), Schloss Dagstuhl, Germany},
  year         = {2006}
}
@article{DBLP:journals/anor/Muramatsu05,
  author       = {Masakazu Muramatsu},
  title        = {A Unified Class of Directly Solvable Semidefinite Programming Problems},
  journal      = {Ann. Oper. Res.},
  volume       = {133},
  number       = {1-4},
  pages        = {85--97},
  year         = {2005}
}
@article{DBLP:journals/coap/BraunM05,
  author       = {Stephen Braun and
                  John E. Mitchell},
  title        = {A Semidefinite Programming Heuristic for Quadratic Programming Problems
                  with Complementarity Constraints},
  journal      = {Comput. Optim. Appl.},
  volume       = {31},
  number       = {1},
  pages        = {5--29},
  year         = {2005}
}
@article{DBLP:journals/ieicet/FujieT05,
  author       = {Tetsuya Fujie and
                  Akihisa Tamura},
  title        = {A Semidefinite Programming Relaxation for the Generalized Stable Set
                  Problem},
  journal      = {{IEICE} Trans. Fundam. Electron. Commun. Comput. Sci.},
  volume       = {88-A},
  number       = {5},
  pages        = {1122--1128},
  year         = {2005}
}
@article{DBLP:journals/mp/Anjos05,
  author       = {Miguel F. Anjos},
  title        = {An improved semidefinite programming relaxation for the satisfiability
                  problem},
  journal      = {Math. Program.},
  volume       = {102},
  number       = {3},
  pages        = {589--608},
  year         = {2005}
}
@inproceedings{DBLP:conf/aaim/SuzukaMYM05,
  author       = {Ayami Suzuka and
                  Ryuhei Miyashiro and
                  Akiko Yoshise and
                  Tomomi Matsui},
  title        = {Semidefinite Programming Based Approaches to Home-Away Assignment
                  Problems in Sports Scheduling},
  booktitle    = {{AAIM}},
  series       = {Lecture Notes in Computer Science},
  volume       = {3521},
  pages        = {95--103},
  publisher    = {Springer},
  year         = {2005}
}
@inproceedings{DBLP:conf/ipco/SoZY05,
  author       = {Anthony Man{-}Cho So and
                  Jiawei Zhang and
                  Yinyu Ye},
  title        = {On Approximating Complex Quadratic Optimization Problems via Semidefinite
                  Programming Relaxations},
  booktitle    = {{IPCO}},
  series       = {Lecture Notes in Computer Science},
  volume       = {3509},
  pages        = {125--135},
  publisher    = {Springer},
  year         = {2005}
}
@inproceedings{DBLP:conf/or/AnjosV05,
  author       = {Miguel F. Anjos and
                  Anthony Vannelli},
  title        = {On the Computational Performance of a Semidefinite Programming Approach
                  to Single Row Layout Problems},
  booktitle    = {{OR}},
  pages        = {277--282},
  year         = {2005}
}
@article{DBLP:journals/jco/Roupin04,
  author       = {Fr{\'{e}}d{\'{e}}ric Roupin},
  title        = {From Linear to Semidefinite Programming: An Algorithm to Obtain Semidefinite
                  Relaxations for Bivalent Quadratic Problems},
  journal      = {J. Comb. Optim.},
  volume       = {8},
  number       = {4},
  pages        = {469--493},
  year         = {2004}
}
@article{DBLP:journals/jcss/GoemansW04,
  author       = {Michel X. Goemans and
                  David P. Williamson},
  title        = {Approximation algorithms for M\({}_{\mbox{AX}}\)-3-C\({}_{\mbox{UT}}\)
                  and other problems via complex semidefinite programming},
  journal      = {J. Comput. Syst. Sci.},
  volume       = {68},
  number       = {2},
  pages        = {442--470},
  year         = {2004}
}
@article{DBLP:journals/mmor/Anjos04,
  author       = {Miguel F. Anjos},
  title        = {On semidefinite programming relaxations for the satisfiability problem},
  journal      = {Math. Methods Oper. Res.},
  volume       = {60},
  number       = {3},
  pages        = {349--367},
  year         = {2004}
}
@article{DBLP:journals/mp/BensonV03,
  author       = {Hande Y. Benson and
                  Robert J. Vanderbei},
  title        = {Solving Problems with Semidefinite and Related Constraints Using Interior-Point
                  Methods for Nonlinear Programming},
  journal      = {Math. Program.},
  volume       = {95},
  number       = {2},
  pages        = {279--302},
  year         = {2003}
}
@article{DBLP:journals/mp/Parrilo03,
  author       = {Pablo A. Parrilo},
  title        = {Semidefinite programming relaxations for semialgebraic problems},
  journal      = {Math. Program.},
  volume       = {96},
  number       = {2},
  pages        = {293--320},
  year         = {2003}
}
@article{DBLP:journals/oms/XuYZ03,
  author       = {Dachuan Xu and
                  Yinyu Ye and
                  Jiawei Zhang},
  title        = {Approximating the 2-catalog segmentation problem using semidefinite
                  programming relaxations},
  journal      = {Optim. Methods Softw.},
  volume       = {18},
  number       = {6},
  pages        = {705--719},
  year         = {2003}
}
@inproceedings{DBLP:conf/birthday/ChazelleKS03,
  author       = {Bernard Chazelle and
                  Carl Kingsford and
                  Mona Singh},
  title        = {The Side-Chain Positioning Problem: {A} Semidefinite Programming Formulation
                  With New Rounding Schemes},
  booktitle    = {{PCK50}},
  pages        = {86--94},
  publisher    = {{ACM}},
  year         = {2003}
}
@inproceedings{DBLP:conf/cdc/Vandenberghe0WH03,
  author       = {Lieven Vandenberghe and
                  V. Balakrishnan and
                  Ragnar Wallin and
                  Anders Hansson},
  title        = {On the implementation of primal-dual interior-point methods for semidefinite
                  programming problems derived from the {KYP} lemma},
  booktitle    = {{CDC}},
  pages        = {4658--4663},
  publisher    = {{IEEE}},
  year         = {2003}
}
@inproceedings{DBLP:conf/cp/Hoeve03,
  author       = {Willem Jan van Hoeve},
  title        = {A Hybrid Constraint Programming and Semidefinite Programming Approach
                  for the Stabe Set Problem},
  booktitle    = {{CP}},
  series       = {Lecture Notes in Computer Science},
  volume       = {2833},
  pages        = {407--421},
  publisher    = {Springer},
  year         = {2003}
}
@phdthesis{DBLP:phd/basesearch/Fraticelli02,
  author       = {Barbara M. P. Fraticelli},
  title        = {Semidefinite Cuts and Partial Convexification Techniques with Applications
                  to Continuous Nonconvex Optimization, Stochastic Integer Programming,
                  and Facility Layout Problems},
  school       = {Virginia Tech, Blacksburg, VA, {USA}},
  year         = {2002}
}
@article{DBLP:journals/coap/GruberR02,
  author       = {Gerald Gruber and
                  Franz Rendl},
  title        = {Computational Experience with Ill-Posed Problems in Semidefinite Programming},
  journal      = {Comput. Optim. Appl.},
  volume       = {21},
  number       = {2},
  pages        = {201--212},
  year         = {2002}
}
@article{DBLP:journals/dam/WolkowiczA02,
  author       = {Henry Wolkowicz and
                  Miguel F. Anjos},
  title        = {Semidefinite programming for discrete optimization and matrix completion
                  problems},
  journal      = {Discret. Appl. Math.},
  volume       = {123},
  number       = {1-3},
  pages        = {513--577},
  year         = {2002}
}
@article{DBLP:journals/jgo/BomzeK02,
  author       = {Immanuel M. Bomze and
                  Etienne de Klerk},
  title        = {Solving Standard Quadratic Optimization Problems via Linear, Semidefinite
                  and Copositive Programming},
  journal      = {J. Glob. Optim.},
  volume       = {24},
  number       = {2},
  pages        = {163--185},
  year         = {2002}
}
@article{DBLP:journals/siamjo/LeibfritzM02,
  author       = {Friedemann Leibfritz and
                  El{-}Sayed M. E. Mostafa},
  title        = {An Interior Point Constrained Trust Region Method for a Special Class
                  of Nonlinear Semidefinite Programming Problems},
  journal      = {{SIAM} J. Optim.},
  volume       = {12},
  number       = {4},
  pages        = {1048--1074},
  year         = {2002}
}
@inproceedings{DBLP:conf/stoc/GoemansW01,
  author       = {Michel X. Goemans and
                  David P. Williamson},
  title        = {Approximation algorithms for {MAX-3-CUT} and other problems via complex
                  semidefinite programming},
  booktitle    = {{STOC}},
  pages        = {443--452},
  publisher    = {{ACM}},
  year         = {2001}
}
@article{DBLP:journals/informs/KarischRC00,
  author       = {Stefan E. Karisch and
                  Franz Rendl and
                  Jens Clausen},
  title        = {Solving Graph Bisection Problems with Semidefinite Programming},
  journal      = {{INFORMS} J. Comput.},
  volume       = {12},
  number       = {3},
  pages        = {177--191},
  year         = {2000}
}
@article{DBLP:journals/jar/KlerkMW00,
  author       = {Etienne de Klerk and
                  Hans van Maaren and
                  Joost P. Warners},
  title        = {Relaxations of the Satisfiability Problem Using Semidefinite Programming},
  journal      = {J. Autom. Reason.},
  volume       = {24},
  number       = {1/2},
  pages        = {37--65},
  year         = {2000}
}
@article{DBLP:journals/jco/HelmbergRW00,
  author       = {Christoph Helmberg and
                  Franz Rendl and
                  Robert Weismantel},
  title        = {A Semidefinite Programming Approach to the Quadratic Knapsack Problem},
  journal      = {J. Comb. Optim.},
  volume       = {4},
  number       = {2},
  pages        = {197--215},
  year         = {2000}
}
@article{DBLP:journals/coap/AlfakihKW99,
  author       = {Abdo Y. Alfakih and
                  Amir Khandani and
                  Henry Wolkowicz},
  title        = {Solving Euclidean Distance Matrix Completion Problems Via Semidefinite
                  Programming},
  journal      = {Comput. Optim. Appl.},
  volume       = {12},
  number       = {1-3},
  pages        = {13--30},
  year         = {1999}
}
@article{DBLP:journals/dam/WolkowiczZ99,
  author       = {Henry Wolkowicz and
                  Qing Zhao},
  title        = {Semidefinite Programming Relaxations for the Graph Partitioning Problem},
  journal      = {Discret. Appl. Math.},
  volume       = {96-97},
  pages        = {461--479},
  year         = {1999}
}
@inproceedings{DBLP:conf/ipco/CvetkovicCK99,
  author       = {Dragos M. Cvetkovic and
                  Mirjana Cangalovic and
                  Vera Kovacevic{-}Vujcic},
  title        = {Semidefinite Programming Methods for the Symmetric Traveling Salesman
                  Problem},
  booktitle    = {{IPCO}},
  series       = {Lecture Notes in Computer Science},
  volume       = {1610},
  pages        = {126--136},
  publisher    = {Springer},
  year         = {1999}
}
@inproceedings{DBLP:conf/stoc/Zwick99a,
  author       = {Uri Zwick},
  title        = {Outward Rotations: {A} Tool for Rounding Solutions of Semidefinite
                  Programming Relaxations, with Applications to {MAX} {CUT} and Other
                  Problems},
  booktitle    = {{STOC}},
  pages        = {679--687},
  publisher    = {{ACM}},
  year         = {1999}
}
@article{DBLP:journals/jco/ZhaoKRW98,
  author       = {Qing Zhao and
                  Stefan E. Karisch and
                  Franz Rendl and
                  Henry Wolkowicz},
  title        = {Semidefinite Programming Relaxations for the Quadratic Assignment
                  Problem},
  journal      = {J. Comb. Optim.},
  volume       = {2},
  number       = {1},
  pages        = {71--109},
  year         = {1998}
}
@article{DBLP:journals/jacm/GoemansW95,
  author       = {Michel X. Goemans and
                  David P. Williamson},
  title        = {Improved Approximation Algorithms for Maximum Cut and Satisfiability
                  Problems Using Semidefinite Programming},
  journal      = {J. {ACM}},
  volume       = {42},
  number       = {6},
  pages        = {1115--1145},
  year         = {1995}
}
@inproceedings{DBLP:conf/cocoon/BacikM95,
  author       = {Roman Bacik and
                  Sanjeev Mahajan},
  title        = {Semidefinite Programming and its Applications to {NP} Problems},
  booktitle    = {{COCOON}},
  series       = {Lecture Notes in Computer Science},
  volume       = {959},
  pages        = {566--575},
  publisher    = {Springer},
  year         = {1995}
}
@article{DBLP:journals/eccc/ECCC-TR95-011,
  author       = {Roman Bacik and
                  Sanjeev Mahajan},
  title        = {Semidefinite Programming and its Applications to {NP} Problems},
  journal      = {Electron. Colloquium Comput. Complex.},
  volume       = {{TR95-011}},
  year         = {1995}
}
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