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Integral Transformation for Box-Constrained Global Optimization of Decomposable Functions

Seppo Pulkkinen, Marko M. Mäkelä, Napsu Karmitsa, Integral Transformation for Box-Constrained Global Optimization of Decomposable Functions. TUCS Technical Reports 1036, Turku Centre for Computer Science, 2012.

Abstract:

A commonly used approach for solving unconstrained, highly multimodal, distance geometry problems is to use an integral transformation to gradually transform the objective function into a function with a smaller number of undesired local minima. In many cases, an iterative tracing of minimizers of the transformed functions back to the original function via continuation leads to a global minimum of the original objective function. This paper gives a theoretical framework for such a method that is
applicable to box-constrained problems. By assuming decomposability of the objective function (i.e.\ that it can be decomposed into products of univariate functions), we prove the convergence of the proposed method to a KKT point satisfying the first-order necessary and the second-order sufficient optimality conditions of a box-constrained problem. We also give the conditions that guarantee the convergence to the solution from the interior of the feasible domain.

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BibTeX entry:

@TECHREPORT{tPuMaKa12a,
  title = {Integral Transformation for Box-Constrained Global Optimization of Decomposable Functions},
  author = {Pulkkinen, Seppo and Mäkelä, Marko M. and Karmitsa, Napsu},
  number = {1036},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2012},
  keywords = {global optimization, bounds for variables, continuation, Gaussian transform, barrier method, KKT conditions},
  ISBN = {978-952-12-2716-5},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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