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5.2 Solving Symbolic Functions for Particular Variables. 5.1 Solving Algebraic Equations With a Single Variable. 4.2 Using Functions with Symbolic Matrices as Inputs. 4.1 Substituting Values into Symbolic Variables. 1 Introduction to the Symbolic Math Toolbox. Patches and add-ons written by other people:įor formulating and solving optimization problems subject to one-dimensionalįor a pre-processing facial reduction step. Related Patches and Add-OnsThe following are some Please drop us a line, to the bibtex entry, for citation: = , If you use SOSTOOLS for research purposes, we'd be happy to hear about it and Please send email to: You can also do this on GitHub. Semidefinite programming relaxations for semialgebraicįor more references please see but also the authors' websites.įor comments, bug reports, encouragement, suggestions, complaints, etc.,. Structured Semidefinite Programs and Semialgebraic Geometry Methods in. Programming, as well as references to related work, please see: The software has been written and is maintained by:įor a detailed explanation of the theory and applications of sums of squares User's guide (also included with the standard distribution). Performance and to reduce the amount of memory needed.ĭetailed installation instructions are available in the SOSTOOLS It utilizes MATLAB sparse matrix representation for good
SOSTOOLS can easily be run on Windows or MAC OSX machines.
On how to install them, you are referred to their installation These solvers and their documentation can be downloaded for free.
An SDP solver, either SeDuMi, SDPT3, CSDP, SDPNAL, SDPNAL+, CDCS, SDPA and MOSEK. MATLAB Symbolic Math Toolbox version 2.1.2 (optional) for SOSTOOLS versions 2.05 and earlier, or the current version of the MATLAB Symbolic Math Toolbox for SOSTOOLS version 3.00 and later. 
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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