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Post-Optimal Analysis of Linear Semi-Infinite Programs

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Optimization and Optimal Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 39))

Summary

Linear semi-infinite programming (LSIP) deals with linear optimization problems in which either the dimension of the decision space or the number of constraints (but not both) is infinite. In most applications of LSIP to statistics, electronics, telecommunications, and other fields, all the data (or at least part of them) are uncertain. Post-optimal analysis provides answer to questions about the quantitative impact on the optimal value of small perturbations of the data (sensitivity analysis) and also about the continuity properties of the optimal value, the optimal set, and the feasible set (stability analysis) around the nominal problem. This chapter surveys the state of the art in sensitivity and stability analysis in LSIP.

This work was supported by MICINN of Spain, Grant MTM2008-06695- C03-01.

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Acknowledgment

The author wishes to thank M.J. Cánovas, M.D. Fajardo, and J. Parra for their valuable comments and suggestions.

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  1. Department of Statistics and Operations Research, University of Alicante, 03080, Alicante, Spain

    M.A. Goberna

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    Altannar Chinchuluun

  2. Dept. Industrial & Systems, Engineering, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

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  4. Labo. PRISM, Université Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Ider Tseveendorj

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Goberna, M. (2010). Post-Optimal Analysis of Linear Semi-Infinite Programs. In: Chinchuluun, ., Pardalos, P., Enkhbat, R., Tseveendorj, I. (eds) Optimization and Optimal Control. Springer Optimization and Its Applications(), vol 39. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89496-6_2

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