Global minimization of rational functions and the nearest GCDs

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.

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