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Conjugate Duality and the Control of Linear Discrete Systems

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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.

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Acknowledgements

R.I. Boţ research was partially supported by DFG (German Research Foundation), project BO 2516/4-1.

E.R. Csetnek research was supported by DFG (German Research Foundation), project BO 2516/4-1.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria

    Radu Ioan Boţ

  2. Department of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Ernö Robert Csetnek

Authors
  1. Radu Ioan Boţ
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  2. Ernö Robert Csetnek
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Correspondence to Radu Ioan Boţ.

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Boţ, R.I., Csetnek, E.R. Conjugate Duality and the Control of Linear Discrete Systems. J Optim Theory Appl 159, 576–589 (2013). https://doi.org/10.1007/s10957-013-0373-x

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  • DOI: https://doi.org/10.1007/s10957-013-0373-x

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