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.
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Gert Wanka, Radu Ioan Boţ, S. M. Grad, Multiobjective Duality for Convex Semidefinite Programming Problems. Z. Anal. Anwend. 22 (2003), no. 3, pp. 711–728DOI 10.4171/ZAA/1169