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Conjugate Duality and the Control of Linear Discrete Systems

Author

Listed:
  • Radu Ioan Boţ

    (University of Vienna)

  • Ernö Robert Csetnek

    (Chemnitz University of Technology)

Abstract

In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal–dual pair necessary and sufficient optimality conditions. We also discuss the existence of optimal solutions for the primal and dual problems by using duality arguments. The theoretical results are applied in the context of the control of linear discrete systems.

Suggested Citation

  • Radu Ioan Boţ & Ernö Robert Csetnek, 2013. "Conjugate Duality and the Control of Linear Discrete Systems," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 576-589, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-013-0373-x
    DOI: 10.1007/s10957-013-0373-x
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    References listed on IDEAS

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    1. Fujita, Masahisa, 1974. "Duality and maximum principle in multi-period convex programming," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 295-326, December.
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    Cited by:

    1. Hocine Mokhtar-Kharroubi, 2017. "Convex and convex-like optimization over a range inclusion problem and first applications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 277-299, November.

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