Supporting global numerical optimization of rational functions by generic symbolic convexity tests

Authors:
Winfried Neun;Thomas Sturm;Stefan Vigerske
Affiliations:
Zuse Institute Berlin, Berlin, Germany;Dpto. de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain;Department of Mathematics, Humboldt University Berlin, Berlin, Germany
Venue:
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Year:
2010

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Abstract

Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system Reduce. Our long term goal is to integrate Reduce as a "workhorse" for symbolic computations into a numerical solver.