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Feasible partition problem in reverse convex and convex mixed-integer programming

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  • Obuchowska, Wiesława T.

Abstract

In this paper we consider the consistent partition problem in reverse convex and convex mixed-integer programming. In particular we will show that for the considered classes of convex functions, both integer and relaxed systems can be partitioned into two disjoint subsystems, each of which is consistent and defines an unbounded region. The polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided.

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  • 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.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:129-137
    DOI: 10.1016/j.ejor.2013.10.041
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, December.
    6. Wiesława Obuchowska, 2010. "Minimal infeasible constraint sets in convex integer programs," Journal of Global Optimization, Springer, vol. 46(3), pages 423-433, March.
    7. 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.
    8. Obuchowska, Wiesława T., 2012. "Feasibility in reverse convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 58-67.
    9. Chakravarti, Nilotpal, 1994. "Some results concerning post-infeasibility analysis," European Journal of Operational Research, Elsevier, vol. 73(1), pages 139-143, February.
    10. John W. Chinneck & Erik W. Dravnieks, 1991. "Locating Minimal Infeasible Constraint Sets in Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 157-168, May.
    11. H. Tuy & T. V. Thieu & Ng. Q. Thai, 1985. "A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 498-514, August.
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    Cited by:

    1. Wiesława T. Obuchowska, 2015. "Irreducible Infeasible Sets in Convex Mixed-Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 747-766, September.

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