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An outcome space approach for generalized convex multiplicative programs

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Abstract

This paper addresses the problem of minimizing an arbitrary finite sum of products of two convex functions over a convex set. Nonconvex problems in this form constitute a class of generalized convex multiplicative problems. Convex analysis results allow to reformulate the problem as an indefinite quadratic problem with infinitely many linear constraints. Special properties of the quadratic problem combined with an adequate outer approximation procedure for handling its semi-infinite constrained set enable an efficient constraint enumeration global optimization algorithm for generalized convex multiplicative programs. Computational experiences illustrate the proposed approach.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Mato Grosso do Sul, PO Box 549, Campo Grande, MS, 79070-900, Brazil

    Rúbia M. Oliveira

  2. Faculty of Electrical and Computer Engineering, University of Campinas, PO Box 6101, Campinas, SP, 13083-852, Brazil

    Paulo A. V. Ferreira

Authors
  1. Rúbia M. Oliveira
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  2. Paulo A. V. Ferreira
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Correspondence to Paulo A. V. Ferreira.

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Oliveira, R.M., Ferreira, P.A.V. An outcome space approach for generalized convex multiplicative programs. J Glob Optim 47, 107–118 (2010). https://doi.org/10.1007/s10898-009-9460-9

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  • DOI: https://doi.org/10.1007/s10898-009-9460-9

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