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First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems

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Book cover Semi-Infinite Programming

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

Abstract

In this paper we discuss finite dimensional optimization problems subject to an infinite number of inequality constraints (semi-infinite programming problems). We study such problems in a general framework of optimization problems subject to constraints formulated in a form of cone inclusions. General results on duality, and first and second order optimality conditions are presented and specified to considered semi-infinite programming problems. Finally some recent results on quantitative stability and sensitivity analysis of parameterized semi-infinite programming problems are discussed.

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Authors and Affiliations

  1. Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, Georgia, 30332-0205, USA

    Alexander Shapiro

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  1. Alexander Shapiro
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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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Shapiro, A. (1998). First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems. 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_4

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  • DOI: https://doi.org/10.1007/978-1-4757-2868-2_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4795-6

  • Online ISBN: 978-1-4757-2868-2

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