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Feasibility in reverse convex mixed-integer programming

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  • Obuchowska, Wiesława T.

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.

Suggested Citation

  • Obuchowska, Wiesława T., 2012. "Feasibility in reverse convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 58-67.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:1:p:58-67
    DOI: 10.1016/j.ejor.2011.10.011
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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. Herbert E. Scarf, 2008. "An observation on the structure of production sets with indivisibilities," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 1, pages 1-5, Palgrave Macmillan.
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    5. 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.
    6. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, December.
    7. Wiesława Obuchowska, 2010. "Minimal infeasible constraint sets in convex integer programs," Journal of Global Optimization, Springer, vol. 46(3), pages 423-433, March.
    8. 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.
    9. John W. Chinneck, 2008. "Feasibility and Infeasibility in Optimization," International Series in Operations Research and Management Science, Springer, number 978-0-387-74932-7, December.
    10. Chakravarti, Nilotpal, 1994. "Some results concerning post-infeasibility analysis," European Journal of Operational Research, Elsevier, vol. 73(1), pages 139-143, February.
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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.
    2. 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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