Journal of Optimization Theory and Applications

, Volume 159, Issue 3, pp 576–589 | Cite as

Conjugate Duality and the Control of Linear Discrete Systems

  • Radu Ioan Boţ
  • Ernö Robert Csetnek


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.


Convex optimization Conjugate duality Control of linear systems 



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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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsChemnitz University of TechnologyChemnitzGermany

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