Multiobjective Duality for Convex Semidefinite Programming Problems | Zendy

Gert Wanka | Zendy; Radu Ioan Boţ | Zendy; SorinMihai Grad | Zendy

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Multiobjective Duality for Convex Semidefinite Programming Problems

Author(s) -

Gert Wanka,

Radu Ioan Boţ,

SorinMihai Grad

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1169

Subject(s) - duality (order theory) , strong duality , semidefinite programming , weak duality , converse , perturbation function , mathematics , wolfe duality , duality gap , convex optimization , mathematical optimization , regular polygon , convex analysis , optimization problem , combinatorics , geometry

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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