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Somayeh Sojoudi
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2020 – today
- 2023
- [j24]Salar Fattahi
, Cédric Josz
, Yuhao Ding
, Reza Mohammadi-Ghazi
, Javad Lavaei
, Somayeh Sojoudi
:
On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization. IEEE Trans. Autom. Control. 68(1): 80-95 (2023) - [i33]Jingqi Li, Chih-Yuan Chiu, Lasse Peters, Somayeh Sojoudi, Claire J. Tomlin, David Fridovich-Keil:
Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories. CoRR abs/2301.01398 (2023) - 2022
- [j23]Sangwoo Park
, Elizabeth Glista
, Javad Lavaei
, Somayeh Sojoudi
:
An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality. IEEE Access 10: 124960-124978 (2022) - [j22]Igor Molybog, Somayeh Sojoudi, Javad Lavaei
:
Role of sparsity and structure in the optimization landscape of non-convex matrix sensing. Math. Program. 193(1): 75-111 (2022) - [j21]Fernando Gama
, Somayeh Sojoudi:
Distributed linear-quadratic control with graph neural networks. Signal Process. 196: 108506 (2022) - [c62]Ziye Ma, Yingjie Bi, Javad Lavaei, Somayeh Sojoudi:
Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements. AAAI 2022: 7672-7681 - [c61]Baturalp Yalcin, Haixiang Zhang, Javad Lavaei, Somayeh Sojoudi:
Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods. AISTATS 2022: 319-341 - [c60]Yatong Bai, Tanmay Gautam, Yu Gai, Somayeh Sojoudi:
Practical Convex Formulations of One-hidden-layer Neural Network Adversarial Training. ACC 2022: 1535-1542 - [c59]Dimitris Papadimitriou, Somayeh Sojoudi:
Control and Uncertainty Propagation in the Presence of Outliers by Utilizing Student-t Process Regression. ACC 2022: 2748-2754 - [c58]Samuel Pfrommer, Somayeh Sojoudi:
LQR Control with Sparse Adversarial Disturbances. CDC 2022: 2346-2353 - [c57]Tanmay Gautam, Brendon G. Anderson, Somayeh Sojoudi, Laurent El Ghaoui:
A Sequential Greedy Approach for Training Implicit Deep Models. CDC 2022: 2751-2758 - [c56]Fengjun Yang, Fernando Gama, Somayeh Sojoudi, Nikolai Matni:
Distributed Optimal Control of Graph Symmetric Systems via Graph Filters. CDC 2022: 5245-5252 - [c55]Brendon G. Anderson, Somayeh Sojoudi:
Certified Robustness via Locally Biased Randomized Smoothing. L4DC 2022: 207-220 - [c54]Samuel Pfrommer, Tanmay Gautam, Alec Zhou, Somayeh Sojoudi:
Safe Reinforcement Learning with Chance-constrained Model Predictive Control. L4DC 2022: 291-303 - [i32]Yatong Bai, Tanmay Gautam, Somayeh Sojoudi:
Efficient Global Optimization of Two-layer ReLU Networks: Quadratic-time Algorithms and Adversarial Training. CoRR abs/2201.01965 (2022) - [i31]Ziye Ma, Somayeh Sojoudi:
Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate. CoRR abs/2203.03899 (2022) - [i30]Jingqi Li, Donggun Lee, Somayeh Sojoudi, Claire J. Tomlin:
Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learning. CoRR abs/2203.10142 (2022) - [i29]Brendon G. Anderson, Tanmay Gautam, Somayeh Sojoudi:
An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Models. CoRR abs/2208.07464 (2022) - [i28]Baturalp Yalcin, Ziye Ma, Javad Lavaei, Somayeh Sojoudi:
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing. CoRR abs/2208.07469 (2022) - [i27]Samuel Pfrommer, Somayeh Sojoudi:
LQR Control with Sparse Adversarial Disturbances. CoRR abs/2209.10629 (2022) - [i26]Fengjun Yang, Fernando Gama, Somayeh Sojoudi, Nikolai Matni:
Distributed Optimal Control of Graph Symmetric Systems via Graph Filters. CoRR abs/2210.15847 (2022) - 2021
- [j20]Salar Fattahi
, Somayeh Sojoudi
:
Sample Complexity of Block-Sparse System Identification Problem. IEEE Trans. Control. Netw. Syst. 8(4): 1905-1917 (2021) - [j19]Ming Jin
, Javad Lavaei
, Somayeh Sojoudi
, Ross Baldick
:
Boundary Defense Against Cyber Threat for Power System State Estimation. IEEE Trans. Inf. Forensics Secur. 16: 1752-1767 (2021) - [c53]Ming Jin, Heng Chang, Wenwu Zhu, Somayeh Sojoudi:
Power up! Robust Graph Convolutional Network via Graph Powering. AAAI 2021: 8004-8012 - [c52]Mohammad Mahdi Khalili, Xueru Zhang, Mahed Abroshan, Somayeh Sojoudi:
Improving Fairness and Privacy in Selection Problems. AAAI 2021: 8092-8100 - [c51]Igor Molybog, Somayeh Sojoudi, Javad Lavaei:
No Spurious Solutions in Non-convex Matrix Sensing: Structure Compensates for Isometry. ACC 2021: 2587-2594 - [c50]Jingqi Li, David Fridovich-Keil, Somayeh Sojoudi, Claire J. Tomlin:
Augmented Lagrangian Method for Instantaneously Constrained Reinforcement Learning Problems. CDC 2021: 2982-2989 - [c49]Heng Chang, Yu Rong, Tingyang Xu, Wenbing Huang, Somayeh Sojoudi, Junzhou Huang, Wenwu Zhu:
Spectral Graph Attention Network with Fast Eigen-approximation. CIKM 2021: 2905-2909 - [c48]Ziye Ma, Somayeh Sojoudi:
A Sequential Framework Towards an Exact SDP Verification of Neural Networks. DSAA 2021: 1-8 - [c47]Fernando Gama, Somayeh Sojoudi:
Graph Neural Networks for Distributed Linear-Quadratic Control. L4DC 2021: 111-124 - [i25]Brendon G. Anderson, Ziye Ma, Jingqi Li, Somayeh Sojoudi:
Partition-Based Convex Relaxations for Certifying the Robustness of ReLU Neural Networks. CoRR abs/2101.09306 (2021) - [i24]Fernando Gama, Somayeh Sojoudi:
Distributed Linear-Quadratic Control with Graph Neural Networks. CoRR abs/2103.08417 (2021) - [i23]Ziye Ma, Yingjie Bi, Javad Lavaei, Somayeh Sojoudi:
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements. CoRR abs/2105.08232 (2021) - [i22]Yatong Bai, Tanmay Gautam, Yu Gai, Somayeh Sojoudi:
Practical Convex Formulation of Robust One-hidden-layer Neural Network Training. CoRR abs/2105.12237 (2021) - [i21]Fernando Gama, Brendon G. Anderson, Somayeh Sojoudi:
Node-Variant Graph Filters in Graph Neural Networks. CoRR abs/2106.00089 (2021) - [i20]Baturalp Yalcin, Haixiang Zhang, Javad Lavaei, Somayeh Sojoudi:
Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods. CoRR abs/2110.10279 (2021) - [i19]Samuel Pfrommer, Tanmay Gautam, Alec Zhou, Somayeh Sojoudi:
Safe Reinforcement Learning with Chance-constrained Model Predictive Control. CoRR abs/2112.13941 (2021) - 2020
- [j18]Fariba Zohrizadeh, Cédric Josz, Ming Jin, Ramtin Madani, Javad Lavaei, Somayeh Sojoudi:
A survey on conic relaxations of optimal power flow problem. Eur. J. Oper. Res. 287(2): 391-409 (2020) - [j17]Salar Fattahi, Somayeh Sojoudi:
Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis. J. Mach. Learn. Res. 21: 59:1-59:51 (2020) - [j16]Salar Fattahi, Nikolai Matni, Somayeh Sojoudi:
Efficient Learning of Distributed Linear-Quadratic Control Policies. SIAM J. Control. Optim. 58(5): 2927-2951 (2020) - [c46]Sangwoo Park, Elizabeth Glista, Javad Lavaei, Somayeh Sojoudi:
Homotopy Method for Finding the Global Solution of Post-contingency Optimal Power Flow. ACC 2020: 1830-1837 - [c45]Sangwoo Park, Elizabeth Glista
, Javad Lavaei, Somayeh Sojoudi:
Homotopy Method for Finding the Global Solution of Post-contingency Optimal Power Flow. ACC 2020: 3126-3133 - [c44]Salar Fattahi, Cédric Josz, Reza Mohammadi-Ghazi, Javad Lavaei, Somayeh Sojoudi:
Absence of Spurious Local Trajectories in Time-Varying Optimization: A Control-Theoretic Perspective. CCTA 2020: 140-147 - [c43]Elizabeth Glista
, Somayeh Sojoudi:
Convex model to evaluate worst-case performance of local search in the Optimal Power Flow problem. CDC 2020: 1691-1697 - [c42]Brendon G. Anderson, Ziye Ma, Jingqi Li, Somayeh Sojoudi:
Tightened Convex Relaxations for Neural Network Robustness Certification. CDC 2020: 2190-2197 - [c41]Fangda Gu, Heng Chang, Wenwu Zhu, Somayeh Sojoudi, Laurent El Ghaoui:
Implicit Graph Neural Networks. NeurIPS 2020 - [i18]Heng Chang, Yu Rong, Tingyang Xu, Wenbing Huang, Somayeh Sojoudi, Junzhou Huang, Wenwu Zhu:
Spectral Graph Attention Network. CoRR abs/2003.07450 (2020) - [i17]Brendon G. Anderson, Ziye Ma, Jingqi Li, Somayeh Sojoudi:
Tightened Convex Relaxations for Neural Network Robustness Certification. CoRR abs/2004.00570 (2020) - [i16]Fangda Gu, Heng Chang, Wenwu Zhu, Somayeh Sojoudi, Laurent El Ghaoui:
Implicit Graph Neural Networks. CoRR abs/2009.06211 (2020) - [i15]Brendon G. Anderson, Somayeh Sojoudi:
Data-Driven Assessment of Deep Neural Networks with Random Input Uncertainty. CoRR abs/2010.01171 (2020) - [i14]Brendon G. Anderson, Somayeh Sojoudi:
Certifying Neural Network Robustness to Random Input Noise from Samples. CoRR abs/2010.07532 (2020) - [i13]Ziye Ma, Somayeh Sojoudi:
Strengthened SDP Verification of Neural Network Robustness via Non-Convex Cuts. CoRR abs/2010.08603 (2020) - [i12]Fernando Gama, Somayeh Sojoudi:
Graph Neural Networks for Distributed Linear-Quadratic Control. CoRR abs/2011.05360 (2020) - [i11]Mohammad Mahdi Khalili, Xueru Zhang, Mahed Abroshan, Somayeh Sojoudi:
Improving Fairness and Privacy in Selection Problems. CoRR abs/2012.03812 (2020)
2010 – 2019
- 2019
- [j15]Salar Fattahi, Richard Y. Zhang, Somayeh Sojoudi
:
Linear-Time Algorithm for Learning Large-Scale Sparse Graphical Models. IEEE Access 7: 12658-12672 (2019) - [j14]Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi:
Conic optimization for control, energy systems, and machine learning: Applications and algorithms. Annu. Rev. Control. 47: 323-340 (2019) - [j13]Salar Fattahi, Somayeh Sojoudi:
Graphical Lasso and Thresholding: Equivalence and Closed-form Solutions. J. Mach. Learn. Res. 20: 10:1-10:44 (2019) - [j12]Richard Y. Zhang, Somayeh Sojoudi, Javad Lavaei:
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery. J. Mach. Learn. Res. 20: 114:1-114:34 (2019) - [j11]Somayeh Sojoudi, Salar Fattahi, Javad Lavaei
:
Convexification of generalized network flow problem. Math. Program. 173(1-2): 353-391 (2019) - [c40]Brendon G. Anderson, Somayeh Sojoudi:
Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation. Allerton 2019: 965-972 - [c39]Somayeh Sojoudi, Benjamin Recht, John C. Doyle:
Mathematical Models of Physiological Responses to Exercise. ACC 2019: 1525-1532 - [c38]Salar Fattahi, Nikolai Matni, Somayeh Sojoudi:
Learning Sparse Dynamical Systems from a Single Sample Trajectory. CDC 2019: 2682-2689 - [c37]Nan Tian, Ajay Kumar Tanwani, Jinfa Chen, Mas Ma, Robert Zhang, Bill Huang, Ken Goldberg, Somayeh Sojoudi:
A Fog Robotic System for Dynamic Visual Servoing. ICRA 2019: 1982-1988 - [c36]Cédric Josz, Daniel K. Molzahn, Matteo Tacchi
, Somayeh Sojoudi:
Transient Stability Analysis of Power Systems via Occupation Measures. ISGT 2019: 1-5 - [c35]Nan Tian, Ajay Kumar Tanwani, Ken Goldberg, Somayeh Sojoudi:
Mitigating Network Latency in Cloud-Based Teleoperation Using Motion Segmentation and Synthesis. ISRR 2019: 906-921 - [i10]Richard Y. Zhang, Somayeh Sojoudi, Javad Lavaei:
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery. CoRR abs/1901.01631 (2019) - [i9]Salar Fattahi, Nikolai Matni, Somayeh Sojoudi:
Learning Sparse Dynamical Systems from a Single Sample Trajectory. CoRR abs/1904.09396 (2019) - [i8]Ming Jin, Heng Chang, Wenwu Zhu, Somayeh Sojoudi:
Power up! Robust Graph Convolutional Network against Evasion Attacks based on Graph Powering. CoRR abs/1905.10029 (2019) - [i7]Brendon G. Anderson, Somayeh Sojoudi:
Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation. CoRR abs/1907.04409 (2019) - [i6]Salar Fattahi, Nikolai Matni, Somayeh Sojoudi:
Efficient Learning of Distributed Linear-Quadratic Controllers. CoRR abs/1909.09895 (2019) - 2018
- [c34]Salar Fattahi, Somayeh Sojoudi:
Data-Driven Sparse System Identification. Allerton 2018: 462-469 - [c33]Salar Fattahi, Somayeh Sojoudi:
Closed-Form Solution and Sparsity Path for Inverse Covariance Estimation Problem. ACC 2018: 410-417 - [c32]Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi:
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms. ACC 2018: 798-815 - [c31]Nan Tian, Benjamin Kuo, Xinhe Ren, Michael Yu, Robert Zhang, Bill Huang, Ken Goldberg, Somayeh Sojoudi:
A Cloud-Based Robust Semaphore Mirroring System for Social Robots. CASE 2018: 1351-1358 - [c30]Salar Fattahi, Somayeh Sojoudi:
Non-Asymptotic Analysis of Block-Regularized Regression Problem. CDC 2018: 27-34 - [c29]Salar Fattahi, Richard Y. Zhang, Somayeh Sojoudi:
Sparse Inverse Covariance Estimation for Chordal Structures. ECC 2018: 837-844 - [c28]Richard Y. Zhang, Salar Fattahi, Somayeh Sojoudi:
Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion. ICML 2018: 5761-5770 - [c27]Cédric Josz, Yi Ouyang, Richard Y. Zhang, Javad Lavaei, Somayeh Sojoudi:
A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization. NeurIPS 2018: 2446-2454 - [c26]Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi, Javad Lavaei:
How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery? NeurIPS 2018: 5591-5602 - [i5]Richard Y. Zhang, Salar Fattahi, Somayeh Sojoudi:
Linear-Time Algorithm for Learning Large-Scale Sparse Graphical Models. CoRR abs/1802.04911 (2018) - [i4]Salar Fattahi, Somayeh Sojoudi:
Data-Driven Sparse System Identification. CoRR abs/1803.07753 (2018) - [i3]Richard Y. Zhang, Cédric Josz, Somayeh Sojoudi, Javad Lavaei:
How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery? CoRR abs/1805.10251 (2018) - [i2]Nan Tian, Jinfa Chen, Mas Ma, Robert Zhang, Bill Huang, Ken Goldberg, Somayeh Sojoudi:
A Fog Robotic System for Dynamic Visual Servoing. CoRR abs/1809.06716 (2018) - [i1]Salar Fattahi, Somayeh Sojoudi:
Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Robust Principal Component Analysis. CoRR abs/1812.11466 (2018) - 2017
- [j10]Ramtin Madani, Somayeh Sojoudi, Ghazal Fazelnia, Javad Lavaei:
Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization. SIAM J. Optim. 27(2): 725-758 (2017) - 2016
- [j9]Somayeh Sojoudi:
Equivalence of Graphical Lasso and Thresholding for Sparse Graphs. J. Mach. Learn. Res. 17: 115:1-115:21 (2016) - [c25]Somayeh Sojoudi:
Graphical lasso and thresholding: Conditions for equivalence. CDC 2016: 7042-7048 - 2014
- [j8]Somayeh Sojoudi, Javad Lavaei:
Exactness of Semidefinite Relaxations for Nonlinear Optimization Problems with Underlying Graph Structure. SIAM J. Optim. 24(4): 1746-1778 (2014) - [j7]Somayeh Sojoudi, Steven H. Low, John C. Doyle:
Buffering Dynamics and Stability of Internet Congestion Controllers. IEEE/ACM Trans. Netw. 22(6): 1808-1818 (2014) - [c24]Somayeh Sojoudi, John Doyle:
Study of the brain functional network using synthetic data. Allerton 2014: 350-357 - [c23]Somayeh Sojoudi:
Equivalence of graphical lasso and thresholding for sparse graphs. Allerton 2014: 1019-1025 - [c22]Somayeh Sojoudi, Ramtin Madani, Ghazal Fazelnia, Javad Lavaei:
Graph-theoretic algorithms for polynomial optimization problems. CDC 2014: 2257-2271 - [c21]Ramtin Madani, Ghazal Fazelnia, Somayeh Sojoudi, Javad Lavaei:
Low-rank solutions of matrix inequalities with applications to polynomial optimization and matrix completion problems. CDC 2014: 4328-4335 - 2013
- [c20]Ramtin Madani, Somayeh Sojoudi, Javad Lavaei:
Convex relaxation for optimal power flow problem: Mesh networks. ACSSC 2013: 1375-1382 - [c19]Somayeh Sojoudi, Javad Lavaei:
Study of nonlinear power optimization problems using algebraic graph theory. CAMSAP 2013: 424-427 - [c18]Somayeh Sojoudi, Javad Lavaei:
On the exactness of semidefinite relaxation for nonlinear optimization over graphs: Part I. CDC 2013: 1043-1050 - [c17]Somayeh Sojoudi, Javad Lavaei:
On the exactness of semidefinite relaxation for nonlinear optimization over graphs: Part II. CDC 2013: 1051-1057 - [c16]Somayeh Sojoudi, Javad Lavaei:
Convexification of Generalized Network Flow problem with application to power systems. CDC 2013: 7552-7559 - [c15]Somayeh Sojoudi, Ramtin Madani, Javad Lavaei:
Low-rank solution of convex relaxation for optimal power flow problem. SmartGridComm 2013: 636-641 - [c14]Somayeh Sojoudi, Javad Lavaei:
Convexification of optimal power flow problem by means of phase shifters. SmartGridComm 2013: 756-761 - 2012
- [c13]Javad Lavaei, Somayeh Sojoudi:
Competitive equilibria in electricity markets with nonlinearities. ACC 2012: 3081-3088 - 2011
- [c12]Somayeh Sojoudi, Javad Lavaei, Richard M. Murray:
Fault-tolerant controller design with applications in power systems and synthetic biology. ACC 2011: 4135-4142 - [c11]Somayeh Sojoudi, Steven H. Low, John C. Doyle:
Effect of buffers on stability of Internet congestion controllers. INFOCOM 2011: 471-475 - 2010
- [j6]Somayeh Sojoudi, Amir G. Aghdam:
Interconnection-based performance analysis for a class of decentralized controllers. Autom. 46(5): 796-803 (2010) - [j5]Javad Lavaei, Somayeh Sojoudi, Amir G. Aghdam:
Pole Assignment With Improved Control Performance by Means of Periodic Feedback. IEEE Trans. Autom. Control. 55(1): 248-252 (2010) - [j4]Javad Lavaei, Somayeh Sojoudi:
Time Complexity of Decentralized Fixed-Mode Verification. IEEE Trans. Autom. Control. 55(4): 971-976 (2010) - [c10]Javad Lavaei, Somayeh Sojoudi, Richard M. Murray:
Simple delay-based implementation of continuous-time controllers. ACC 2010: 5781-5788 - [c9]Javad Lavaei, Somayeh Sojoudi, Richard M. Murray
:
Synthesis of embedded control systems with high sampling frequencies. CDC 2010: 7606-7612
2000 – 2009
- 2009
- [j3]Somayeh Sojoudi, Amir G. Aghdam:
Overlapping control systems with optimal information exchange. Autom. 45(5): 1176-1181 (2009) - [j2]Somayeh Sojoudi, Javad Lavaei, Amir G. Aghdam:
Robust controllability and observability degrees of polynomially uncertain systems. Autom. 45(11): 2640-2645 (2009) - [c8]Javad Lavaei, Somayeh Sojoudi:
Complexity of checking the existence of a stabilizing decentralized controller. ACC 2009: 1827-1832 - [c7]Somayeh Sojoudi, Javad Lavaei, Amir G. Aghdam:
Controllability and observability of uncertain systems: A robust measure. CDC 2009: 4180-4186 - 2008
- [c6]Somayeh Sojoudi, Amir G. Aghdam:
Performance analysis for a class of decentralized control systems. ACC 2008: 710-716 - 2007
- [j1]Somayeh Sojoudi, Javad Lavaei, Amir G. Aghdam:
Robust Stabilizability Verification of Polynomially Uncertain LTI Systems. IEEE Trans. Autom. Control. 52(9): 1721-1726 (2007) - [c5]Somayeh Sojoudi, Javad Lavaei, Amir G. Aghdam:
Optimal Information Flow Structure for Control of Interconnected Systems. ACC 2007: 1508-1513 - [c4]Javad Lavaei, Somayeh Sojoudi, Amir G. Aghdam:
Stability Criterion for General Proper Systems with Constrained Control Structure. ACC 2007: 1648-1653 - [c3]Javad Lavaei, Somayeh Sojoudi, Amir G. Aghdam:
Pole assignment with improved control performance by means of periodic feedback. CDC 2007: 1082-1087 - [c2]Somayeh Sojoudi, Amir G. Aghdam:
Characterizing all classes of LTI stabilizing structurally constrained controllers by means of combinatorics. CDC 2007: 4415-4420 - [c1]Javad Lavaei, Somayeh Sojoudi, Amir G. Aghdam:
Rational optimization using sum-of-squares techniques. CDC 2007: 4723-4730