2024/09/27 by Torbjørn Cunis, Cunis, Torbjørn, Jan Olucak +1 · 4 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Blind Source Separation Techniques #FOS: Electrical engineering #FOS: Mathematics #Neural Networks and Applications #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2409.18549
openalex publication_date 2024/09/27 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28
We present CaΣoS, 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. CaΣoS 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. CaΣoS is available open-source at https://github.com/ifr-acso/casos.