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On the Solution of Generalized Multiplicative Extremum Problems

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Abstract

The paper addresses the problem of maximizing a sum of products of positive and concave real-valued functions over a convex feasible set. A reformulation based on the image of the feasible set through the vector-valued function which describes the problem, combined with an adequate application of convex analysis results, lead to an equivalent indefinite quadratic extremum problem with infinitely many linear constraints. Special properties of this later problem allow to solve it by an efficient relaxation algorithm. Some numerical tests illustrate the approach proposed.

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Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, State University of Campinas, Av. Albert Einstein, 400, 13083-852, Campinas, SP, Brazil

    Alireza M. Ashtiani & Paulo A. V. Ferreira

Authors
  1. Alireza M. Ashtiani
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  2. Paulo A. V. Ferreira
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Corresponding author

Correspondence to Paulo A. V. Ferreira.

Additional information

This work was partially sponsored by grants from the “Conselho Nacional de Pesquisa e Desenvolvimento”, CNPq, Brazil.

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Ashtiani, A.M., Ferreira, P.A.V. On the Solution of Generalized Multiplicative Extremum Problems. J Optim Theory Appl 149, 411–419 (2011). https://doi.org/10.1007/s10957-010-9782-2

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