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Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming

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  • M.J. Cánovas
  • M.A. López
  • J. Parra
  • M.I. Todorov

Abstract

In this paper we introduce the concept of solving strategy for a linear semi-infinite programming problem, whose index set is arbitrary and whose coefficient functions have no special property at all. In particular, we consider two strategies which either approximately solve or exactly solve the approximating problems, respectively. Our principal aim is to establish a global framework to cope with different concepts of well-posedness spread out in the literature. Any concept of well-posedness should entail different properties of these strategies, even in the case that we are not assuming the boundedness of the optimal set. In the paper we consider three desirable properties, leading to an exhaustive study of them in relation to both strategies. The more significant results are summarized in a table, which allows us to show the double goal of the paper. On the one hand, we characterize the main features of each strategy, in terms of certain stability properties (lower and upper semicontinuity) of the feasible set mapping, optimal value function and optimal set mapping. On the other hand, and associated with some cells of the table, we recognize different notions of Hadamard well-posedness. We also provide an application to the analysis of the Hadamard well-posedness for a linear semi-infinite formulation of the Lagrangian dual of a nonlinear programming problem. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • M.J. Cánovas & M.A. López & J. Parra & M.I. Todorov, 2001. "Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming," Annals of Operations Research, Springer, vol. 101(1), pages 171-190, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:171-190:10.1023/a:1010920507183
    DOI: 10.1023/A:1010920507183
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    Cited by:

    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. Canovas, M.J. & Lopez, M.A. & Parra, J. & Toledo, F.J., 2007. "Sufficient conditions for total ill-posedness in linear semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1126-1136, September.
    3. Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.
    4. María J. Cánovas & Marco A. López & Juan Parra, 2002. "Stability in the Discretization of a Parametric Semi-Infinite Convex Inequality System," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 755-774, November.

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