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

Please always quote using this URN: urn:nbn:de:0297-zib-11644
  • 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.

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Author:Winfried Neun, Thomas Sturm, Stefan Vigerske
Document Type:ZIB-Report
Tag:Convex Functions; Hybrid Symbolic-Numeric Computation; Nonlinear Global Optimization; Real Quantifier Elimination
Date of first Publication:2010/02/08
Series (Serial Number):ZIB-Report (10-01)
Published in:App. in: CASC 2010, Proceedings, Vladimir P. Gerdt (ed.) Springer 2010, LNCS 6244, pp. 205-219