Approximation and Optimization of Polyhedral Discrete and Differential Inclusions (original) (raw)

Abstract

In the first part of the paperoptimization of polyhedral discrete and differential inclusions is considered, the problem is reduced to convex minimization problem and the necessary and sufficient condition for optimality is derived. The optimality conditions for polyhedral differential inclusions based on discrete-approximation problem according to continuous problems are formulated. In particular, boundedness of the set of adjoint discrete solutions and upper semicontinuity of the locally adjoint mapping are proved. In the second part of paper an optimization problem described by convex inequality constraint is studied. By using the equivalence theorem concerning the subdifferential calculus and approximating method necessary and sufficient condition for discrete-approximation problem with inequality constraint is established.

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Authors and Affiliations

  1. Industrial Engineering Department Faculty of Management, Istanbul Technical University, 34367, Maçka, Istanbul, Turkey
    Elimhan N. Mahmudov

Authors

  1. Elimhan N. Mahmudov

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Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy
    Salvatore Greco & Benedetto Matarazzo &
  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France
    Bernadette Bouchon-Meunier
  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy
    Giulianella Coletti
  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy
    Mario Fedrizzi
  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA
    Ronald R. Yager

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Mahmudov, E.N. (2012). Approximation and Optimization of Polyhedral Discrete and Differential Inclusions. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8\_38

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