Global minimization of rational functions and the nearest GCDs

Authors:
Jiawang Nie;James Demmel;Ming Gu
Affiliations:
Department of Mathematics, University of California, Berkeley, USA 94720;Department of Math & EECS, University of California, Berkeley, USA 94720;Department of Mathematics, University of California, Berkeley, USA 94720
Venue:
Journal of Global Optimization
Year:
2008

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Abstract

This paper discusses the global minimization of rational functions with or without constraints. We propose sum of squares relaxations to solve these problems, and study their properties. Some special features are discussed. First, we consider minimization of rational functions without constraints. Second, as an application, we show how to find the nearest common divisors of polynomials via unconstrained minimization of rational functions. Third, we discuss minimizing rational functions under some constraints which are described by polynomials.