A probabilistic symbolic algorithm to find the minimum of a polynomial function on a basic closed semialgebraic set

2013/04/19 by Gabriela Jeronimo, Jeronimo, Gabriela, Daniel Perrucci +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Polynomial and algebraic computation #math.AG #math.OC #msc:14P10 #msc:14Q20 #msc:68W30

paper · pdf · doi:10.48550/arxiv.1304.5558

arxiv created 2013/04/19 · arxiv updated 2013/04/23

Abstract

We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set E in Rⁿ. We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset E^min of E where the minimum of g is attained, provided that E^min is non-empty and has at least one compact connected component.

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