GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi

Authors:
Didier Henrion;Jean-Bernard Lasserre
Affiliations:
Laboratoire d'Analyse et d'Architecture des Systèmes Centre National de la Recherche Scientifique, Prague, Toulouse, France;Laboratoire d'Analyse et d'Architecture des Systèmes Centre National de la Recherche Scientifique, Toulouse, France
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2003

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Abstract

GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally nonconvex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality, or integer constraints. It generates a series of lower bounds monotonically converging to the global optimum without any problem splitting. Global optimality is detected and isolated optimal solutions are extracted automatically. Numerical experiments show that for most of the small-scale problems described in the literature, the global optimum is reached at low computational cost.