SOSOPT

SOSOPT: A Toolbox for Polynomial Optimization. SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox. Section 1 introduces the problem formulations for SOS tests, SOS feasibility problems, SOS optimizations, and generalized SOS problems. Section 2 reviews the SOSOPT toolbox for solving these optimizations. This section includes information on toolbox installation, formulating constraints, solving SOS optimizations, and setting optimization options. Finally, Section 3 briefly reviews the connections between SOS optimizations and semide?nite programs (SDPs). It is the connection to SDPs that enables SOS optimizations to be solved in an efficient manner


References in zbMATH (referenced in 12 articles )

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  1. Liu, Kairong; Li, Meilun; She, Zhikun: Stability verification for a class of stochastic hybrid systems by semidefinite programming (2021)
  2. Briat, C.: Stability and (L_1 \times\ell_1)-to-(L_1 \times\ell_1) performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays (2020)
  3. Hooshmandi, Kaveh; Bayat, Farhad; Jahed-Motlagh, Mohammad Reza; Jalali, Ali Akbar: Polynomial LPV approach to robust (H_\infty) control of nonlinear sampled-data systems (2020)
  4. Permenter, Frank; Parrilo, Pablo A.: Dimension reduction for semidefinite programs via Jordan algebras (2020)
  5. Papp, Dávid; Yildiz, Sercan: Sum-of-squares optimization without semidefinite programming (2019)
  6. Sidorov, Eric; Zacksenhouse, Miriam: Lyapunov based estimation of the basin of attraction of Poincaré maps with applications to limit cycle walking (2019)
  7. Korda, Milan; Jones, Colin N.: Stability and performance verification of optimization-based controllers (2017)
  8. Korda, Milan; Henrion, Didier; Jones, Colin N.: Controller design and value function approximation for nonlinear dynamical systems (2016)
  9. Wang, Guobin; He, Jifeng; Liu, Jing; Sun, Haiying; Ding, Zuohua; Zhang, Miaomiao: Safety verification of interconnected hybrid systems using barrier certificates (2016)
  10. Dai, Liyun; Xia, Bican: Smaller SDP for SOS decomposition (2015)
  11. Meissen, Chris; Lessard, Laurent; Arcak, Murat; Packard, Andrew K.: Compositional performance certification of interconnected systems using ADMM (2015)
  12. Pfifer, Harald; Seiler, Peter: Integral quadratic constraints for delayed nonlinear and parameter-varying systems (2015)