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On D-Optimality Based Trust Regions for Black-Box Optimization Problems

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Author Info

  • Driessen, L.
  • Brekelmans, R.C.M.
  • Hamers, H.J.M.
  • Hertog, D. den

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we show how techniques from response surface methodology and mathematical programming can be combined into a new sequential derivative-free approach for solving unconstrained deterministic black-box optimization problems.In this sequential derivative-free optimization approach local approximations of the underlying objective function are optimized within a trust region framework.If the points that determine the local approximations are located in such away that the approximations become bad, a geometry improving iteration is carried out instead of an objective improving iteration.We incorporate the D-optimality criterion, well-known in design of experiments, in our approach in two different ways.Firstly, it is used to define a trust region that adapts its shape to the locations of the points in which the objective function has been evaluated.Secondly, it determines an optimal geometry improving point.An attractive feature of our approach is that it is insensitive to affine transformations.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2001-69.

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Date of creation: 2001
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Handle: RePEc:dgr:kubcen:200169

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Web page: http://center.uvt.nl

Related research

Keywords: D-optimality; trust region; derivative free; optimization; affine transformations;

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References

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  1. Brekelmans, R.C.M. & Driessen, L. & Hamers, H.J.M. & Hertog, D. den, 2001. "Constrained Optimization Involving Expensive Function Evaluations: A Sequential Approach," Discussion Paper 2001-87, Tilburg University, Center for Economic Research.
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Cited by:
  1. Brekelmans, R.C.M. & Driessen, L. & Hamers, H.J.M. & Hertog, D. den, 2001. "Constrained Optimization Involving Expensive Function Evaluations: A Sequential Approach," Discussion Paper 2001-87, Tilburg University, Center for Economic Research.
  2. Kleijnen, J.P.C. & Beers, W.C.M. van & Nieuwenhuyse, I. van, 2008. "Constrained Optimization in Simulation: A Novel Approach," Discussion Paper 2008-95, Tilburg University, Center for Economic Research.

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