Journal of Global Optimization

, Volume 44, Issue 2, pp 235–250

A global optimization algorithm for generalized semi-infinite, continuous minimax with coupled constraints and bi-level problems

  • Angelos Tsoukalas
  • Berç Rustem
  • Efstratios N. Pistikopoulos
Article

DOI: 10.1007/s10898-008-9321-y

Cite this article as:
Tsoukalas, A., Rustem, B. & Pistikopoulos, E.N. J Glob Optim (2009) 44: 235. doi:10.1007/s10898-008-9321-y

Abstract

We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality. We use Laplace’s smoothing technique and a simulated annealing approach for the solution of these problems. We present computational examples for all three problem classes.

Keywords

Generalized semi-infinite Minimax Bi-level Globaloptimization Min-max-min 

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Angelos Tsoukalas
    • 1
  • Berç Rustem
    • 1
  • Efstratios N. Pistikopoulos
    • 2
  1. 1.Department of ComputingImperial CollegeLondonUK
  2. 2.Centre for Process Systems EngineeringImperial CollegeLondonUK

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