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Complexity Results for Some Global Optimization Problems

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  • M. Locatelli

    (Università di Torino)

Abstract

We discuss the complexity of a class of highly structured global optimization problems, namely the maximization of separable functions, with each one-dimensional component convex and nondecreasing, over polytopes defined by a 0-1 constraint matrix with at most two variables involved in each constraint. In particular, we prove some inapproximability and approximability results.

Suggested Citation

  • M. Locatelli, 2009. "Complexity Results for Some Global Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 93-102, January.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9448-5
    DOI: 10.1007/s10957-008-9448-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Other publications TiSEM 88640b6d-5240-472d-8669-4, Tilburg University, School of Economics and Management.
    4. NESTEROV, Yu, 2003. "Random walk in a simplex and quadratic optimization over convex polytopes," LIDAM Discussion Papers CORE 2003071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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