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Approximation algorithm for a class of global optimization problems

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  • Marco Locatelli

Abstract

In this paper we develop and derive the computational cost of an $${\varepsilon}$$ -approximation algorithm for a class of global optimization problems, where a suitably defined composition of some ratio functions is minimized over a convex set. The result extends a previous one about a class of Linear Fractional/Multiplicative problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Marco Locatelli, 2013. "Approximation algorithm for a class of global optimization problems," Journal of Global Optimization, Springer, vol. 55(1), pages 13-25, January.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:1:p:13-25
    DOI: 10.1007/s10898-011-9813-z
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    References listed on IDEAS

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    1. Daniele Depetrini & Marco Locatelli, 2009. "A FPTAS for a class of linear multiplicative problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 275-288, November.
    2. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    3. de Klerk, E. & Laurent, M. & Parrilo, P., 2006. "A PTAS for the minimization of polynomials of fixed degree over the simplex," Other publications TiSEM 603897c9-179e-43e4-9e83-6, Tilburg University, School of Economics and Management.
    4. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
    5. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
    7. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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