A Geometric Approach to Global Optimization

Authors:
Stefan Nickel;Anita Schöbel
Affiliations:
Fachbereich Mathematik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany (e-mail: nickel@mathematik.uni-kl.de);Fachbereich Mathematik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany (e-mail: nickel@mathematik.uni-kl.de)
Venue:
Journal of Global Optimization
Year:
1999

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Abstract

In this paper we consider the problem of optimizing a piecewise-linear objective function over a non-convex domain. In particular we do not allow the solution to lie in the interior of a prespecified region R. We discuss the geometrical properties of this problems and present algorithms based on combinatorial arguments. In addition we show how we can construct quite complicated shaped sets R while maintaining the combinatorial properties.