1. Conjugate Duality and the Control of Linear Discrete Systems
- Author
-
Ernö Robert Csetnek and Radu Ioan Boţ
- Subjects
Convex analysis ,Mathematical optimization ,Control and Optimization ,Duality gap ,Fenchel's duality theorem ,Applied Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Duality (optimization) ,Perturbation function ,Management Science and Operations Research ,Weak duality ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,Strong duality ,Wolfe duality ,Applied mathematics ,Mathematics - 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.
- Published
- 2013