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Detecting global optimality and extracting solutions in GloptiPoly. (English) Zbl 1119.93301

Henrion, Didier (ed.) et al., Positive polynomials in control. Berlin: Springer (ISBN 3-540-23948-0/pbk). Lecture Notes in Control and Information Sciences 312, 293-310 (2005).
GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality (LMI) relaxations of non-convex optimization problems with multivariate polynomial objective function and constraints, based on the theory of moments. In contrast with the dual sum-of-squares decompositions of positive polynomials, the theory of moments allows to detect global optimality of an LMI relaxation and extract globally optimal solutions. In this report, we describe and illustrate the numerical linear algebra algorithm implemented in GloptiPoly for detecting global optimality and extracting solutions. We also mention some related heuristics that could be useful to reduce the number of variables in the LMI relaxations.
For the entire collection see [Zbl 1059.93002].

MSC:

93-04 Software, source code, etc. for problems pertaining to systems and control theory
93B40 Computational methods in systems theory (MSC2010)
90C22 Semidefinite programming
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