Solving Global Optimization Problems over Polynomials with GloptiPoly 2.1

GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally non-convex) 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. Global optimality is detected and isolated optimal solutions are extracted automatically. In this paper we first briefly describe the theoretical background underlying the relaxations. Following a small illustrative example of the use of GloptiPoly, we then evaluate its performance on benchmark test examples from global optimization, combinatorial optimization and polynomial systems of equations.