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A Comprehensive Survey of Linear Semi-Infinite Optimization Theory

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Semi-Infinite Programming

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 25))

Abstract

This paper reviews the lineax semi-infinite optimization theory as well as its main foundations, namely, the theory of linear semi-infinite systems. The first part is devoted to existence theorems and geometrical properties of the solution set of a linear semi-infinite system. The second part concerns optimality conditions, geometrical properties of the optimal set and duality theory. Finally, the third part analyzes the well-posedness of the linear semi-infinite programming problem and the stability (or continuity properties) of the feasible set, the optimal set and the optimal value mappings when all the data are perturbed.

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Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Alicante, 03071, Alicante, Spain

    Miguel A. Goberna & Marco A. López

Authors
  1. Miguel A. Goberna
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  2. Marco A. López
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Editors and Affiliations

  1. Institute of Mathematics, Brandenburg Technical University of Cottbus, Germany

    Rembert Reemtsen

  2. Institute of Applied Mathematics, University of Erlangen-Nuremberg, Germany

    Jan-J. Rückmann

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Goberna, M.A., López, M.A. (1998). A Comprehensive Survey of Linear Semi-Infinite Optimization Theory. In: Reemtsen, R., Rückmann, JJ. (eds) Semi-Infinite Programming. Nonconvex Optimization and Its Applications, vol 25. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2868-2_1

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  • DOI: https://doi.org/10.1007/978-1-4757-2868-2_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4795-6

  • Online ISBN: 978-1-4757-2868-2

  • eBook Packages: Springer Book Archive

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