CaΣoS: A nonlinear sum-of-squares optimization suite

Abstract

We present Ca$\Sigma$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates their fast, repeated evaluations. To that extent, we make use of CasADi's symbolic framework and realize concepts of monomial sparsity, linear operators (including duals), and functions between polynomials. Ca$\Sigma$oS currently provides interfaces to the conic solvers SeDuMi, Mosek, and SCS as well as methods to solve quasiconvex optimization problems (via bisection) and nonconvex optimization problems (via sequential convexification). Numerical examples for benchmark problems including region-of-attraction and reachable set estimation for nonlinear dynamic systems demonstrate significant improvements in computation time compared to existing toolboxes. Ca$\Sigma$oS is available open-source at https://github.com/ifr-acso/casos.

arXiv commentSubmitted to 2025 American Control Conference

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