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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 3, 2003, pp. 711–728
DOI: 10.4171/ZAA/1169

Published online: 2003-09-30

Multiobjective Duality for Convex Semidefinite Programming Problems

Gert Wanka[1], Radu Ioan Boţ[2] and S. M. Grad[3]

(1) Technische Universität Chemnitz, Germany
(2) Technische Universität Chemnitz, Germany
(3) University of Cluj-Napoca, Romania

We treat some duality assertions regarding multiobjective convex semidefinite programming problems. Having a vector minimization problem with convex entries in the objective vector function, we establish a dual for it using the so-called conjugacy approach. In order to deal with the duality assertions between these problems we need to study the duality properties and the optimality conditions of the scalarized problem associated to the initial one. Using these results we present the weak, strong and converse duality assertions regarding the primal problem and the dual we obtained for it.

Keywords: Multiobjective duality, semidefinite programming, convex optimization, Pareto efficiency

Wanka Gert, Boţ Radu Ioan, Grad S. M.: Multiobjective Duality for Convex Semidefinite Programming Problems. Z. Anal. Anwend. 22 (2003), 711-728. doi: 10.4171/ZAA/1169