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

  • Authors:

  • Angelos Tsoukalas;Berç Rustem;Efstratios N. Pistikopoulos

  • Affiliations:

  • Department of Computing, Imperial College, London, UK;Department of Computing, Imperial College, London, UK;Centre for Process Systems Engineering, Imperial College, London, UK

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2009

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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.