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

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages16
Volume2001-69
Publication statusPublished - 2001

Publication series

NameCentER Discussion Paper
Volume2001-69

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Derivatives
Geometry
Mathematical programming
Design of experiments

Keywords

  • D-optimality
  • trust region
  • derivative free
  • optimization
  • affine transformations

Cite this

Driessen, L., Brekelmans, R. C. M., Hamers, H. J. M., & den Hertog, D. (2001). On D-Optimality Based Trust Regions for Black-Box Optimization Problems. (CentER Discussion Paper; Vol. 2001-69). Tilburg: Operations research.
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Driessen, L, Brekelmans, RCM, Hamers, HJM & den Hertog, D 2001 'On D-Optimality Based Trust Regions for Black-Box Optimization Problems' CentER Discussion Paper, vol. 2001-69, Operations research, Tilburg.

On D-Optimality Based Trust Regions for Black-Box Optimization Problems. / Driessen, L.; Brekelmans, R.C.M.; Hamers, H.J.M.; den Hertog, D.

Tilburg : Operations research, 2001. (CentER Discussion Paper; Vol. 2001-69).

Research output: Working paperDiscussion paperOther research output

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T1 - On D-Optimality Based Trust Regions for Black-Box Optimization Problems

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N2 - 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.

AB - 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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KW - optimization

KW - affine transformations

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Driessen L, Brekelmans RCM, Hamers HJM, den Hertog D. On D-Optimality Based Trust Regions for Black-Box Optimization Problems. Tilburg: Operations research. 2001. (CentER Discussion Paper).