An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems

Article

DOI: 10.1007/s10957-008-9473-4

Cite this article as:
Parpas, P. & Rustem, B. J Optim Theory Appl (2009) 141: 461. doi:10.1007/s10957-008-9473-4

Abstract

We propose an algorithm for the global optimization of continuous minimax problems involving polynomials. The method can be described as a discretization approach to the well known semi-infinite formulation of the problem. We proceed by approximating the infinite number of constraints using tools and techniques from semidefinite programming. We then show that, under appropriate conditions, the SDP approximation converges to the globally optimal solution of the problem. We also discuss the numerical performance of the method on some test problems.

Keywords

Worst case analysis Continuous minimax algorithms Semidefinite programming Global optimization 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of ComputingImperial CollegeLondonUK

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