Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
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Antonis Papachristodoulou | Giovanni Fantuzzi | Yang Zheng | A. Papachristodoulou | Yang Zheng | Giovanni Fantuzzi
[1] L. Vandenberghe,et al. Bregman primal–dual first-order method and application to sparse semidefinite programming , 2021, Computational Optimization and Applications.
[2] P. Parrilo,et al. On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones , 2021, Mathematical Programming.
[3] Keqiang Li,et al. Leading Cruise Control in Mixed Traffic Flow: System Modeling, Controllability, and String Stability , 2020, IEEE Transactions on Intelligent Transportation Systems.
[4] Santanu S. Dey,et al. Sparse PSD approximation of the PSD cone , 2020, Math. Program..
[5] Gangshan Jing,et al. Angle-Based Sensor Network Localization , 2019, IEEE Transactions on Automatic Control.
[6] Antonis Papachristodoulou,et al. Decomposed Structured Subsets for Semidefinite and Sum-of-Squares Optimization , 2019, ArXiv.
[7] A. Papachristodoulou,et al. Block Factor-Width-Two Matrices and Their Applications to Semidefinite and Sum-of-Squares Optimization , 2019, IEEE Transactions on Automatic Control.
[8] D. Henrion,et al. Exploiting Sparsity for Semi-Algebraic Set Volume Computation , 2019, Foundations of Computational Mathematics.
[9] Mario Sznaier,et al. Peak Estimation Recovery and Safety Analysis , 2021, IEEE Control Systems Letters.
[10] Alec Jacobson,et al. Surface multigrid via intrinsic prolongation , 2021, ACM Trans. Graph..
[11] Jie Wang,et al. TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization , 2021, ArXiv.
[12] A. Wynn,et al. Bounds on heat transport for convection driven by internal heating , 2021, Journal of Fluid Mechanics.
[13] Bican Xia,et al. Choosing the Variable Ordering for Cylindrical Algebraic Decomposition via Exploiting Chordal Structure , 2021, ISSAC.
[14] Giovanni Fantuzzi,et al. Sum-of-squares chordal decomposition of polynomial matrix inequalities , 2020, Mathematical Programming.
[15] Victor Magron,et al. Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension , 2020, SIAM J. Optim..
[16] J. Lasserre,et al. TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity , 2019, SIAM Journal on Optimization.
[17] Volkan Cevher,et al. Scalable Semidefinite Programming , 2019, SIAM J. Math. Data Sci..
[18] Michal Kocvara. Decomposition of arrow type positive semidefinite matrices with application to topology optimization , 2021, Math. Program..
[19] Akiko Yoshise,et al. Polyhedral approximations of the semidefinite cone and their application , 2019, Computational Optimization and Applications.
[20] Mark Cannon,et al. COSMO: A Conic Operator Splitting Method for Convex Conic Problems , 2019, Journal of Optimization Theory and Applications.
[21] Chenqi Mou,et al. Chordal Graphs in Triangular Decomposition in Top-Down Style , 2018, J. Symb. Comput..
[22] Didier Henrion,et al. Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes , 2018, J. Nonlinear Sci..
[23] Javad Lavaei,et al. Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion , 2017, Mathematical Programming.
[24] Alessio Lomuscio,et al. Efficient Neural Network Verification via Layer-based Semidefinite Relaxations and Linear Cuts , 2021, IJCAI.
[25] Antonis Papachristodoulou,et al. Exploiting Sparsity for Neural Network Verification , 2021, L4DC.
[26] Milan Korda,et al. Sparse moment-sum-of-squares relaxations for nonlinear dynamical systems with guaranteed convergence , 2020, 2012.05572.
[27] Herbert Werner,et al. Distributed Controller Design for Systems Interconnected over Chordal Graphs , 2020, 2020 American Control Conference (ACC).
[28] Richard Y. Zhang. On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples , 2020, NeurIPS.
[29] Heng Yang,et al. One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers , 2020, NeurIPS.
[30] Juan Pablo Vielma,et al. Towards practical generic conic optimization. , 2020 .
[31] Paul Rolland,et al. Lipschitz constant estimation of Neural Networks via sparse polynomial optimization , 2020, ICLR.
[32] Victor Magron,et al. Semialgebraic Optimization for Lipschitz Constants of ReLU Networks , 2020, NeurIPS.
[33] J. Lasserre,et al. Approximating regions of attraction of a sparse polynomial differential system , 2019, IFAC-PapersOnLine.
[34] Mark Cannon,et al. A clique graph based merging strategy for decomposable SDPs. , 2019 .
[35] A. Papachristodoulou,et al. On the Existence of Block-Diagonal Solutions to Lyapunov and ${\mathcal {H}_\infty }$ Riccati Inequalities , 2019, IEEE Transactions on Automatic Control.
[36] Amir Ali Ahmadi,et al. A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics , 2019, Annu. Rev. Control. Robotics Auton. Syst..
[37] Giovanni Fantuzzi,et al. Bounding Extreme Events in Nonlinear Dynamics Using Convex Optimization , 2019, SIAM J. Appl. Dyn. Syst..
[38] Maryam Kamgarpour,et al. Sparsity Invariance for Convex Design of Distributed Controllers , 2019, IEEE Transactions on Control of Network Systems.
[39] Yang Zheng,et al. Smoothing Traffic Flow via Control of Autonomous Vehicles , 2018, IEEE Internet of Things Journal.
[40] Alden Waters,et al. Rank Optimality for the Burer-Monteiro Factorization , 2018, SIAM J. Optim..
[41] D. Goluskin. Bounding extrema over global attractors using polynomial optimisation , 2018, Nonlinearity.
[42] Kim-Chuan Toh,et al. SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0) , 2017, Optim. Methods Softw..
[43] Maryam Kamgarpour,et al. Distributed Design for Decentralized Control Using Chordal Decomposition and ADMM , 2017, IEEE Transactions on Control of Network Systems.
[44] Yang Zheng,et al. Chordal decomposition in operator-splitting methods for sparse semidefinite programs , 2017, Mathematical Programming.
[45] Cheng-Hsiung Yang,et al. Exploiting Sparsity in SDP Relaxation for Harmonic Balance Method , 2020, IEEE Access.
[46] Mohammad Abuabiah,et al. Recovery of Binary Sparse Signals From Compressed Linear Measurements via Polynomial Optimization , 2019, IEEE Signal Processing Letters.
[47] Antonis Papachristodoulou,et al. Chordal Decomposition in Rank Minimized Semidefinite Programs with Applications to Subspace Clustering , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).
[48] Maryam Kamgarpour,et al. On Separable Quadratic Lyapunov Functions for Convex Design of Distributed Controllers , 2019, 2019 18th European Control Conference (ECC).
[49] Cho-Jui Hsieh,et al. A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks , 2019, NeurIPS.
[50] Matthew M. Peet,et al. Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets , 2019 .
[51] Bican Xia,et al. A New Sparse SOS Decomposition Algorithm Based on Term Sparsity , 2018, ISSAC.
[52] Yang Zheng,et al. Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials , 2018, 2019 American Control Conference (ACC).
[53] Joachim Dahl,et al. On the robustness and scalability of semidefinite relaxation for optimal power flow problems , 2018, Optimization and Engineering.
[54] A. Bandeira,et al. Deterministic Guarantees for Burer‐Monteiro Factorizations of Smooth Semidefinite Programs , 2018, Communications on Pure and Applied Mathematics.
[55] Anders Hansson,et al. Efficient Robust Model Predictive Control using Chordality , 2018, 2019 18th European Control Conference (ECC).
[56] Mohamadreza Ahmadi,et al. A framework for input–output analysis of wall-bounded shear flows , 2018, Journal of Fluid Mechanics.
[57] Yang Zheng,et al. Fast ADMM for Sum-of-Squares Programs Using Partial Orthogonality , 2017, IEEE Transactions on Automatic Control.
[58] Amir Ali Ahmadi,et al. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization , 2017, SIAM J. Appl. Algebra Geom..
[59] Didier Henrion,et al. Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systems , 2017, SIAM J. Control. Optim..
[60] Pushmeet Kohli,et al. Efficient Neural Network Verification with Exactness Characterization , 2019, UAI.
[61] Andrea Tramontani,et al. Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks , 2019 .
[62] Yang Zheng,et al. Chordal sparsity in control and optimization of large-scale systems , 2019 .
[63] Javad Lavaei,et al. A Low-Complexity Parallelizable Numerical Algorithm for Sparse Semidefinite Programming , 2018, IEEE Transactions on Control of Network Systems.
[64] Aditi Raghunathan,et al. Semidefinite relaxations for certifying robustness to adversarial examples , 2018, NeurIPS.
[65] Stephen P. Boyd,et al. Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization , 2018, Journal of Optimization Theory and Applications.
[66] Amir Ali Ahmadi,et al. Robust-to-Dynamics Optimization , 2018, ArXiv.
[67] Yang Zheng,et al. Decomposition and Completion of Sum-of-Squares Matrices , 2018, 2018 IEEE Conference on Decision and Control (CDC).
[68] Maryam Kamgarpour,et al. Scalable analysis of linear networked systems via chordal decomposition , 2018, 2018 European Control Conference (ECC).
[69] Yang Zheng,et al. Scalable Design of Structured Controllers Using Chordal Decomposition , 2018, IEEE Transactions on Automatic Control.
[70] Salar Fattahi,et al. Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion , 2018, ICML.
[71] A. Hansson,et al. Exploiting chordality in optimization algorithms for model predictive control , 2017, 1711.10254.
[72] A. Wynn,et al. Bounds on heat transfer for Bénard–Marangoni convection at infinite Prandtl number , 2017, Journal of Fluid Mechanics.
[73] Yu Zhang,et al. Conic Relaxations for Power System State Estimation With Line Measurements , 2017, IEEE Transactions on Control of Network Systems.
[74] Jean B. Lasserre,et al. Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity , 2016, Mathematical Programming Computation.
[75] Anders Rantzer,et al. Distributed Semidefinite Programming With Application to Large-Scale System Analysis , 2015, IEEE Transactions on Automatic Control.
[76] Pablo A. Parrilo,et al. Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone , 2014, Math. Program..
[77] Yang Zheng,et al. Decomposition Methods for Large-Scale Semidefinite Programs with Chordal Aggregate Sparsity and Partial Orthogonality , 2018 .
[78] Amir Ali Ahmadi,et al. Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).
[79] Amir Beck,et al. First-Order Methods in Optimization , 2017 .
[80] Yang Zheng,et al. Block-diagonal solutions to Lyapunov inequalities and generalisations of diagonal dominance , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).
[81] Yang Zheng,et al. Dynamical Modeling and Distributed Control of Connected and Automated Vehicles: Challenges and Opportunities , 2017, IEEE Intelligent Transportation Systems Magazine.
[82] Frank Permenter,et al. Solving Conic Optimization Problems via Self-Dual Embedding and Facial Reduction: A Unified Approach , 2017, SIAM J. Optim..
[83] Wotao Yin,et al. A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs , 2017, ArXiv.
[84] Isak Nielsen,et al. Distributed primal–dual interior-point methods for solving tree-structured coupled convex problems using message-passing , 2017, Optim. Methods Softw..
[85] Alireza Karimi,et al. Plug-and-Play Voltage Stabilization in Inverter-Interfaced Microgrids via a Robust Control Strategy , 2017, IEEE Transactions on Control Systems Technology.
[86] Javad Lavaei,et al. Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization , 2017, SIAM J. Optim..
[87] Stephen P. Boyd,et al. General Heuristics for Nonconvex Quadratically Constrained Quadratic Programming , 2017, 1703.07870.
[88] Pablo A. Parrilo,et al. Chordal networks of polynomial ideals , 2016, SIAM J. Appl. Algebra Geom..
[89] James Anderson,et al. Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov Functions , 2016, Autom..
[90] Amir Ali Ahmadi,et al. Optimization over structured subsets of positive semidefinite matrices via column generation , 2015, Discret. Optim..
[91] Jean B. Lasserre,et al. A bounded degree SOS hierarchy for polynomial optimization , 2015, EURO J. Comput. Optim..
[92] Xin Jiang,et al. Minimum Rank Positive Semidefinite Matrix Completion with Chordal Sparsity Pattern , 2017 .
[93] Robin Deits,et al. Sum-of-squares optimization in Julia , 2017 .
[94] Mauricio Barahona,et al. Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming , 2016, SIAM J. Sci. Comput..
[95] S. Kim,et al. Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets , 2016, J. Glob. Optim..
[96] Mohamadreza Ahmadi,et al. Stability Analysis for a Class of Partial Differential Equations via Semidefinite Programming , 2016, IEEE Transactions on Automatic Control.
[97] Deqing Huang,et al. Sum-of-squares approach to feedback control of laminar wake flows , 2016, Journal of Fluid Mechanics.
[98] Deqing Huang,et al. Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization , 2015, SIAM J. Appl. Dyn. Syst..
[99] Andrew V. Knyazev,et al. Degeneracy in maximal clique decomposition for Semidefinite Programs , 2015, 2016 American Control Conference (ACC).
[100] Pablo A. Parrilo,et al. Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach , 2014, SIAM J. Discret. Math..
[101] Stephen P. Boyd,et al. Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding , 2013, Journal of Optimization Theory and Applications.
[102] Yvonne Freeh,et al. Interior Point Algorithms Theory And Analysis , 2016 .
[103] Yifan Sun,et al. Decomposition Methods for Sparse Matrix Nearness Problems , 2015, SIAM J. Matrix Anal. Appl..
[104] Javad Lavaei,et al. A fast distributed algorithm for decomposable semidefinite programs , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).
[105] Amir Ali Ahmadi,et al. Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming , 2015, ArXiv.
[106] Antonis Papachristodoulou,et al. Advances in computational Lyapunov analysis using sum-of-squares programming , 2015 .
[107] Yinyu Ye,et al. A homogeneous interior-point algorithm for nonsymmetric convex conic optimization , 2014, Mathematical Programming.
[108] Martin S. Andersen,et al. Chordal Graphs and Semidefinite Optimization , 2015, Found. Trends Optim..
[109] Michael Ulbrich,et al. Distributed Stability Tests for Large-Scale Systems With Limited Model Information , 2015, IEEE Transactions on Control of Network Systems.
[110] Giancarlo Ferrari-Trecate,et al. Plug-and-Play Voltage and Frequency Control of Islanded Microgrids With Meshed Topology , 2014, IEEE Transactions on Smart Grid.
[111] Ian A. Hiskens,et al. Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem , 2014, IEEE Transactions on Power Systems.
[112] Yifan Sun. Decomposition methods for semidefinite optimization , 2015 .
[113] Richard Mason. A chordal sparsity approach to scalable linear and nonlinear systems analysis , 2015 .
[114] Pablo A. Parrilo,et al. Basis selection for SOS programs via facial reduction and polyhedral approximations , 2014, 53rd IEEE Conference on Decision and Control.
[115] Georgios B. Giannakis,et al. Power System Nonlinear State Estimation Using Distributed Semidefinite Programming , 2014, IEEE Journal of Selected Topics in Signal Processing.
[116] Antonis Papachristodoulou,et al. Chordal sparsity, decomposing SDPs and the Lyapunov equation , 2014, 2014 American Control Conference.
[117] Anders Rantzer,et al. Robust Stability Analysis of Sparsely Interconnected Uncertain Systems , 2013, IEEE Transactions on Automatic Control.
[118] Martin S. Andersen,et al. Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems , 2013, IEEE Transactions on Power Systems.
[119] Yifan Sun,et al. Decomposition in Conic Optimization with Partially Separable Structure , 2013, SIAM J. Optim..
[120] Russ Tedrake,et al. Convex optimization of nonlinear feedback controllers via occupation measures , 2013, Int. J. Robotics Res..
[121] Mi-Ching Tsai,et al. Robust and Optimal Control , 2014 .
[122] Michael Ulbrich,et al. Distributed control design with local model information and guaranteed stability , 2014 .
[123] Karl Johan Åström,et al. Control: A perspective , 2014, Autom..
[124] Nathan van de Wouw,et al. Controller Synthesis for String Stability of Vehicle Platoons , 2014, IEEE Transactions on Intelligent Transportation Systems.
[125] Jesse T. Holzer,et al. Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming , 2013, IEEE Transactions on Power Systems.
[126] Qiao Li,et al. Distributed algorithm for SDP state estimation , 2013, 2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT).
[127] Georgios B. Giannakis,et al. Distributed Optimal Power Flow for Smart Microgrids , 2012, IEEE Transactions on Smart Grid.
[128] Colin Neil Jones,et al. Inner Approximations of the Region of Attraction for Polynomial Dynamical Systems , 2012, NOLCOS.
[129] Didier Henrion,et al. Convex Computation of the Region of Attraction of Polynomial Control Systems , 2012, IEEE Transactions on Automatic Control.
[130] Martin S. Andersen,et al. Logarithmic barriers for sparse matrix cones , 2012, Optim. Methods Softw..
[131] Thorsten Theobald,et al. Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization , 2011, Math. Oper. Res..
[132] Rekha R. Thomas,et al. Semidefinite Optimization and Convex Algebraic Geometry , 2012 .
[133] Pablo A. Parrilo,et al. Chapter 3: Polynomial Optimization, Sums of Squares, and Applications , 2012 .
[134] Yurii Nesterov,et al. Towards non-symmetric conic optimization , 2012, Optim. Methods Softw..
[135] Hans-Peter Kriegel,et al. Subspace clustering , 2012, WIREs Data Mining Knowl. Discov..
[136] Antonis Papachristodoulou,et al. A Decomposition Technique for Nonlinear Dynamical System Analysis , 2012, IEEE Transactions on Automatic Control.
[137] R. Jabr. Exploiting Sparsity in SDP Relaxations of the OPF Problem , 2012, IEEE Transactions on Power Systems.
[138] Antonis Papachristodoulou,et al. A Converse Sum of Squares Lyapunov Result With a Degree Bound , 2012, IEEE Transactions on Automatic Control.
[139] David Tse,et al. Distributed algorithms for optimal power flow problem , 2011, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).
[140] Didier Henrion,et al. Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions , 2011, IEEE Transactions on Automatic Control.
[141] Makoto Yamashita,et al. Latest Developments in the SDPA Family for Solving Large-Scale SDPs , 2012 .
[142] Masakazu Kojima,et al. Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion , 2011, Math. Program..
[143] Stephen P. Boyd,et al. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..
[144] Martin S. Andersen. Chordal Sparsity in Interior-Point Methods for Conic Optimization , 2011 .
[145] G. Chesi. Domain of Attraction: Analysis and Control via SOS Programming , 2011 .
[146] Martin S. Andersen,et al. Linear matrix inequalities with chordal sparsity patterns and applications to robust quadratic optimization , 2010, 2010 IEEE International Symposium on Computer-Aided Control System Design.
[147] Naonori Kakimura,et al. A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices , 2010 .
[148] Wotao Yin,et al. Alternating direction augmented Lagrangian methods for semidefinite programming , 2010, Math. Program. Comput..
[149] Masakazu Muramatsu,et al. A facial reduction algorithm for finding sparse SOS representations , 2010, Oper. Res. Lett..
[150] Joachim Dahl,et al. Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones , 2010, Math. Program. Comput..
[151] Didier Henrion,et al. Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations , 2010, 1003.4608.
[152] Etienne de Klerk,et al. Exploiting special structure in semidefinite programming: A survey of theory and applications , 2010, Eur. J. Oper. Res..
[153] Martin S. Andersen,et al. Support vector machine training using matrix completion techniques , 2010 .
[154] M. Mevissen. Sparse semidefinite programming relaxations for large scale polynomial optimization and their applications to differential equations , 2010 .
[155] Ufuk Topcu,et al. Robust Region-of-Attraction Estimation , 2010, IEEE Transactions on Automatic Control.
[156] Kim-Chuan Toh,et al. A Newton-CG Augmented Lagrangian Method for Semidefinite Programming , 2010, SIAM J. Optim..
[157] Federico Poloni. Of Note , 2009 .
[158] Johan Löfberg,et al. Dualize it: software for automatic primal and dual conversions of conic programs , 2009, Optim. Methods Softw..
[159] Johan Löfberg,et al. Pre- and Post-Processing Sum-of-Squares Programs in Practice , 2009, IEEE Transactions on Automatic Control.
[160] Masakazu Kojima,et al. Exploiting Sparsity in SDP Relaxation for Sensor Network Localization , 2009, SIAM J. Optim..
[161] Nobuki Takayama,et al. Solutions of polynomial systems derived from the steady cavity flow problem , 2008, ISSAC '09.
[162] Konrad Schmuedgen. Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas , 2009 .
[163] Didier Henrion,et al. GloptiPoly 3: moments, optimization and semidefinite programming , 2007, Optim. Methods Softw..
[164] Jiawang Nie,et al. Sum of squares method for sensor network localization , 2006, Comput. Optim. Appl..
[165] Yoshio Okamoto,et al. B-453 User's Manual for SparseCoLO: Conversion Methods for SPARSE COnic-form Linear Optimization Problems , 2009 .
[166] Vwani P. Roychowdhury,et al. Covariance selection for nonchordal graphs via chordal embedding , 2008, Optim. Methods Softw..
[167] Masakazu Muramatsu,et al. SparsePOP: a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems , 2005 .
[168] K. Fujisawa,et al. Semidefinite programming for optimal power flow problems , 2008 .
[169] Emmanuel Trélat,et al. Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations , 2007, SIAM J. Control. Optim..
[170] J. Demmel,et al. Sparse SOS Relaxations for Minimizing Functions that are Summations of Small Polynomials , 2006, SIAM J. Optim..
[171] Pablo A. Parrilo,et al. Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma , 2007, 2007 46th IEEE Conference on Decision and Control.
[172] George J. Pappas,et al. A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates , 2007, IEEE Transactions on Automatic Control.
[173] Shazlina Mohamad Shuib. STATE ESTIMATION OF POWER SYSTEMS , 2007 .
[174] Renato D. C. Monteiro,et al. Large-scale semidefinite programming via a saddle point Mirror-Prox algorithm , 2007, Math. Program..
[175] M. Kojima,et al. Solving partial differential equations via sparse SDP relaxations , 2007 .
[176] Antonis Papachristodoulou,et al. Positive Forms and Stability of Linear Time-Delay Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.
[177] David Grimm,et al. A note on the representation of positive polynomials with structured sparsity , 2006, math/0611498.
[178] Akira Tanaka,et al. The worst-case time complexity for generating all maximal cliques and computational experiments , 2006, Theor. Comput. Sci..
[179] Jean B. Lasserre,et al. Convergent SDP-Relaxations in Polynomial Optimization with Sparsity , 2006, SIAM J. Optim..
[180] Carsten W. Scherer,et al. Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs , 2006, Math. Program..
[181] Samuel Burer,et al. Computational enhancements in low-rank semidefinite programming , 2006, Optim. Methods Softw..
[182] Didier Henrion,et al. Convergent relaxations of polynomial matrix inequalities and static output feedback , 2006, IEEE Transactions on Automatic Control.
[183] A. Nemirovski. Advances in convex optimization : conic programming , 2005 .
[184] Masakazu Muramatsu,et al. Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity , 2004 .
[185] Rajesh Rajamani,et al. Vehicle dynamics and control , 2005 .
[186] Ojas D. Parekh,et al. On Factor Width and Symmetric H-matrices , 2005 .
[187] Renato D. C. Monteiro,et al. Digital Object Identifier (DOI) 10.1007/s10107-004-0564-1 , 2004 .
[188] A. Papachristodoulou,et al. A tutorial on sum of squares techniques for systems analysis , 2005, Proceedings of the 2005, American Control Conference, 2005..
[189] A. Garulli,et al. Positive Polynomials in Control , 2005 .
[190] Anthony Man-Cho So,et al. Theory of semidefinite programming for Sensor Network Localization , 2005, SODA '05.
[191] Yurii Nesterov,et al. Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.
[192] A. Papachristodoulou,et al. Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).
[193] Barry W. Peyton,et al. Maximum Cardinality Search for Computing Minimal Triangulations of Graphs , 2004, Algorithmica.
[194] P. Parrilo,et al. Symmetry groups, semidefinite programs, and sums of squares , 2002, math/0211450.
[195] J. Lofberg,et al. YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).
[196] M. Kojima,et al. SDPA-C (SemiDefinite Programming Algorithm - Completion method) User's Manual — Version 6.2.0 , 2004 .
[197] Stephen P. Boyd,et al. Fastest Mixing Markov Chain on a Graph , 2004, SIAM Rev..
[198] Donald Goldfarb,et al. Robust convex quadratically constrained programs , 2003, Math. Program..
[199] Pablo A. Parrilo,et al. Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..
[200] Kim-Chuan Toh,et al. Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..
[201] Katsuki Fujisawa,et al. Exploiting sparsity in semidefinite programming via matrix completion II: implementation and numerical results , 2003, Math. Program..
[202] Renato D. C. Monteiro,et al. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization , 2003, Math. Program..
[203] Pablo A. Parrilo,et al. Semidefinite Programming Relaxations and Algebraic Optimization in Control , 2003, Eur. J. Control.
[204] M. Kojima. Sums of Squares Relaxations of Polynomial Semidefinite Programs , 2003 .
[205] Samuel Burer,et al. Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices , 2003, SIAM J. Optim..
[206] Donald Goldfarb,et al. Second-order cone programming , 2003, Math. Program..
[207] Pablo A. Parrilo,et al. Introducing SOSTOOLS: a general purpose sum of squares programming solver , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..
[208] Pinar Heggernes,et al. Maximum Cardinality Search for Computing Minimal Triangulations , 2002, WG.
[209] Yin Zhang,et al. Digital Object Identifier (DOI) 10.1007/s101070100279 , 2000 .
[210] Stephen P. Boyd,et al. Future directions in control in an information-rich world , 2003 .
[211] Arkadi Nemirovski,et al. Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.
[212] Kazuo Murota,et al. Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework , 2000, SIAM J. Optim..
[213] Mario Innocenti,et al. Autonomous formation flight , 2000 .
[214] Xiong Zhang,et al. Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization , 1999, SIAM J. Optim..
[215] P. Parrilo. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .
[216] Y. Ye,et al. Semidefinite programming relaxations of nonconvex quadratic optimization , 2000 .
[217] Jos F. Sturm,et al. A Matlab toolbox for optimization over symmetric cones , 1999 .
[218] Arkadi Nemirovski,et al. Robust Convex Optimization , 1998, Math. Oper. Res..
[219] Gábor Pataki,et al. On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues , 1998, Math. Oper. Res..
[220] Yinyu Ye,et al. Interior point algorithms: theory and analysis , 1997 .
[221] E. Yaz. Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.
[222] Brian Borchers,et al. SDPLIB 1.1, A Library of Semidefinite Programming Test Problems , 1998 .
[223] Franz Rendl,et al. Semidefinite Programming and Graph Equipartition , 1998 .
[224] Charles R. Johnson,et al. The Real Positive Definite Completion Problem: Cycle Completability , 1996 .
[225] Stephen P. Boyd,et al. Semidefinite Programming , 1996, SIAM Rev..
[226] B. Reznick. Uniform denominators in Hilbert's seventeenth problem , 1995 .
[227] David P. Williamson,et al. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.
[228] Alexander I. Barvinok,et al. Problems of distance geometry and convex properties of quadratic maps , 1995, Discret. Comput. Geom..
[229] Pedro Luis Dias Peres,et al. Decentralized control through parameter space optimization , 1994, Autom..
[230] Shinji Mizuno,et al. An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm , 1994, Math. Oper. Res..
[231] Yurii Nesterov,et al. Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.
[232] B. Peyton,et al. An Introduction to Chordal Graphs and Clique Trees , 1993 .
[233] J. Dancis. Positive semidefinite completions of partial Hermitian matrices , 1992 .
[234] D. Carlson,et al. Block diagonal semistability factors and Lyapunov semistability of block triangular matrices , 1992 .
[235] Stephen P. Boyd,et al. Structured and Simultaneous Lyapunov Functions for System Stability Problems , 1989 .
[236] L. Rodman,et al. Positive semidefinite matrices with a given sparsity pattern , 1988 .
[237] Katta G. Murty,et al. Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..
[238] Tien-Yien Li. Solving polynomial systems , 1987 .
[239] R. Möhring. Algorithmic graph theory and perfect graphs , 1986 .
[240] Robert E. Tarjan,et al. Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..
[241] Charles R. Johnson,et al. Positive definite completions of partial Hermitian matrices , 1984 .
[242] Andreas Griewank,et al. On the existence of convex decompositions of partially separable functions , 1984, Math. Program..
[243] M. Yannakakis. Computing the Minimum Fill-in is NP^Complete , 1981 .
[244] B. Reznick. Extremal PSD forms with few terms , 1978 .
[245] B. Mercier,et al. A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .
[246] R. Glowinski,et al. Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .
[247] D. Rose. Triangulated graphs and the elimination process , 1970 .
[248] D. J. Newman,et al. Arithmetic, Geometric Inequality , 1960 .
[249] D. Hilbert,et al. Ueber die Darstellung definiter Formen als Summe von Formenquadraten , 1888 .
[250] K. Schittkowski,et al. NONLINEAR PROGRAMMING , 2022 .