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Feasibility in reverse convex mixed-integer programming

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  • Obuchowska, Wiesława T.
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    Abstract

    In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility (CF), that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 1 ()
    Pages: 58-67

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:1:p:58-67

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Integer programming; Feasibility; Concave integer minimization; Reverse convex constraints; Sensitivity analysis; Irreducible infeasible sets;

    References

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    1. Chakravarti, Nilotpal, 1994. "Some results concerning post-infeasibility analysis," European Journal of Operational Research, Elsevier, vol. 73(1), pages 139-143, February.
    2. Herbert E. Scarf, 1977. "An Observation on the Structure of Production Sets with Indivisibilities," Cowles Foundation Discussion Papers 453, Cowles Foundation for Research in Economics, Yale University.
    3. Wiesława Obuchowska, 2010. "Unboundedness in reverse convex and concave integer programming," Computational Statistics, Springer, vol. 72(2), pages 187-204, October.
    4. Wiesława Obuchowska, 2007. "Conditions for boundedness in concave programming under reverse convex and convex constraints," Computational Statistics, Springer, vol. 65(2), pages 261-279, April.
    5. 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.
    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.
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    Cited by:
    1. 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.

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