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Conditions for boundedness in concave programming under reverse convex and convex constraints

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  • Wiesława Obuchowska

Abstract

In this paper, we are concerned with the problem of boundedness in the constrained global maximization of a convex function. In particular, we present necessary and sufficient conditions for boundedness of a feasible region defined by reverse convex constraints and we establish sufficient and necessary conditions for existence of an upper bound for a convex objective function defined over the system of concave inequality constraints. We also address the problem of boundedness in the global maximization problem when a feasible region is convex and unbounded. Copyright Springer-Verlag 2007

Suggested Citation

  • Wiesława Obuchowska, 2007. "Conditions for boundedness in concave programming under reverse convex and convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 261-279, April.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:2:p:261-279
    DOI: 10.1007/s00186-006-0110-4
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    References listed on IDEAS

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    1. Obuchowska, W. T. & Murty, K. G., 2001. "Cone of recession and unboundedness of convex functions," European Journal of Operational Research, Elsevier, vol. 133(2), pages 409-415, January.
    2. Caron, R. J. & Obuchowska, W., 1992. "Unboundedness of a convex quadratic function subject to concave and convex quadratic constraints," European Journal of Operational Research, Elsevier, vol. 63(1), pages 114-123, November.
    3. Caron, Richard J. & Obuchowska, Wieslawa T., 1995. "An algorithm to determine boundedness of quadratically constrained convex quadratic programmes," European Journal of Operational Research, Elsevier, vol. 80(2), pages 431-438, January.
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    Cited by:

    1. Wiesława Obuchowska, 2010. "Unboundedness in reverse convex and concave integer programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 187-204, October.
    2. Wiesława Obuchowska, 2008. "On boundedness of (quasi-)convex integer optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 445-467, December.
    3. Obuchowska, Wiesława T., 2014. "Feasible partition problem in reverse convex and convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 235(1), pages 129-137.
    4. Obuchowska, Wiesława T., 2012. "Feasibility in reverse convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 58-67.

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    1. Wiesława Obuchowska, 2010. "Unboundedness in reverse convex and concave integer programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 187-204, October.
    2. Caron, Richard J. & Obuchowska, Wieslawa T., 1996. "Quadratically constrained convex quadratic programmes: faulty feasible regions," European Journal of Operational Research, Elsevier, vol. 94(1), pages 134-142, October.
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    4. Obuchowska, Wieslawa T., 1998. "Infeasibility analysis for systems of quadratic convex inequalities," European Journal of Operational Research, Elsevier, vol. 107(3), pages 633-643, June.
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    6. Caron, Richard J. & Obuchowska, Wieslawa T., 1995. "An algorithm to determine boundedness of quadratically constrained convex quadratic programmes," European Journal of Operational Research, Elsevier, vol. 80(2), pages 431-438, January.
    7. Obuchowska, Wiesława T., 2012. "Feasibility in reverse convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 58-67.

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