Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests

  • Winfried Neun
  • Thomas Sturm
  • Stefan Vigerske
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)

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.

Keywords

Nonlinear Global Optimization Hybrid Symbolic-Numeric Computation Convex Functions Real Quantifier Elimination Implementation Reduce 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Winfried Neun
    • 1
  • Thomas Sturm
    • 2
  • Stefan Vigerske
    • 3
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Dpto. de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain
  3. 3.Department of MathematicsHumboldt University BerlinBerlinGermany

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