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Convexification of polynomial optimization problems by means of monomial patterns

Gennadiy Averkov(gennadiy.averkov***at***ovgu.de)
Benjamin Peters(benjamin.peters***at***ovgu.de)
Sebastian Sager(sager***at***ovgu.de)

Abstract: Convexification is a core technique in global polynomial optimization. Currently, two different approaches compete in practice and in the literature. First, general approaches rooted in nonlinear programming. They are comparitively cheap from a computational point of view, but typically do not provide good (tight) relaxations with respect to bounds for the original problem. Second, approaches based on sum-of-squares and moment relaxations. They are typically computationally expensive, but do provide tight relaxations. In this paper, we embed both kinds of approaches into a unified framework of monomial relaxations. We develop a convexification strategy that allows to trade off the quality of the bounds against computational expenses. Computational experiments show that a combination with a prototype cutting-plane algorithm gives very encouraging results.

Keywords: convexification · cutting-planes · McCormick relaxation · moment problem · nonlinear optimization · polynomial optimization · separation problem · sum-of-squares

Category 1: Nonlinear Optimization (Bound-constrained Optimization )

Category 2: Global Optimization (Theory )

Category 3: Linear, Cone and Semidefinite Programming

Citation: Institut für Mathematische Optimierung, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39108 Magdeburg, Germany, 01/2019

Download: [PDF]

Entry Submitted: 01/16/2019
Entry Accepted: 01/16/2019
Entry Last Modified: 01/16/2019

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