SOSTOOLS release v1.00 (11th April 2002):.SOSTOOLS release v1.01, compatible with MATLAB 6.5 (4th March 2003):.SOSTOOLS release v2.01 (8th Oct 2004):.SOSTOOLS release v2.02, compatible with MATLAB 7.1 (2nd May 2006):.SOSTOOLS release v3.01 (1st July 2016):.SOSTOOLS release v3.03 (1st April 2018, works with MATLAB's Symbolic math toolbox 8.4 and earlier): SOSTOOLS release v3.04 (20th November 2020, works with MATLAB's Symbolic MATLAB toolbox 8.5):.If interested, you'llįind a much more detailed explanation of the toolbox, some of the applications,Īnd the concepts behind it in the SOSTOOLS user's This sum of squares stuff may actually be useful to you. Hopefully, by now you'll be intrigued, and a bit more inclined to think that (or even exact solutions) for all these problems can be foundīy formulating them in a sum of squares optimization framework. Or, more generally, problems that deal with basic semialgebraic sets (setsĭefined by polynomial equalities and inequalities).Īlthough most of these problems are NP-hard, it turns out that useful bounds.

Distinguishing separable from entangled states in quantum systems.Finding Lyapunov or Bendixson-Dulac functions for nonlinear dynamical.

Mixed continuous-discrete optimization.Constrained or unconstrained optimization of polynomial functions.While this looks quite nice, perhaps you are actually interested in more The objective function is linear and the set of feasible u_i is convex. This is a convex optimization problem, since Here, the A_ij(x) are multivariate polynomials, and the decision variables What is a 'sum of squares optimization program'? WhyĪ sum of squares (SOS) program, in the simplest case, has the form: All these are well-known semidefinite programming solvers, with SOSTOOLS handling internallyĪll the necessary reformulations and data conversion. The SOS programs can be solved using SeDuMi, SDPT3, CSDP, SDPNAL, SDPNAL+, CDCS, SDPA and MOSEK. Simple, flexible, and intuitive high-level notation.

SOSTOOLS canīe used to specify and solve sum of squares polynomial problems using a very SOSTOOLS is a free MATLAB toolbox for formulatingĪnd solving sums of squares (SOS) optimization programs. įor the latest release, please visit our GitHub page. SOSTOOLS - A sum of squares optimization toolbox for MATLAB

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