Bot, Radu Ioan ; Wanka, Gert : A New Duality Approach for Multiobjective Convex Optimization Problems

Author(s):

Bot, Radu Ioan
Wanka, Gert

Title:

A New Duality Approach for Multiobjective Convex Optimization Problems

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 6, 2001

Mathematics Subject Classification:

49N15			[ Duality theory ]
90C25			[ Convex programming ]
90C29			[ Multi-objective and goal programming ]

Abstract:

This paper contains a new duality approach for general convex multiobjective programming problems. The vector objective function of the dual problem is represented in closed form by the conjugate functions of the primal objective functions and the functions describing the constraints. The basic idea is to establish a dual problem for the scalarized primal problem different from the dual problems usually considered in optimization, e.g. the Lagrange dual. But this dual problem based on a special perturbation and conjugacy has an adapted form allowing to construct a multiobjective dual problem in a natural way. Weak, strong and converse duality assertions are presented, some special cases show the applicability of the general approach.

Keywords:

multiobjective duality, conjugate duality, Pareto efficiency, converse duality, multiobjective convex optimization

Language:

English

Publication time:

11 / 2001