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Bot, Radu Ioan; Dumitru, Anca; Wanka, Gert : A New Fenchel Dual Problem in Vector Optimization

Bot, Radu Ioan ; Dumitru, Anca ; Wanka, Gert : A New Fenchel Dual Problem in Vector Optimization

Author(s):
Bot, Radu Ioan
Dumitru, Anca
Wanka, Gert
Title:
A New Fenchel Dual Problem in Vector Optimization
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 18, 2006
Mathematics Subject Classification:
49N15 [ Duality theory ]
90C29 [ Multi-objective and goal programming ]
90C46 [ Optimality conditions, duality ]
Abstract:
We introduce a new Fenchel dual problem in vector optimization inspired by the form of the Fenchel dual of the scalarized primal multiobjective problem. For the vector primal and dual problems we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.
Keywords:
conjugate functions, Fenchel duality, vector optimization, weak and strong duality
Language:
English
Publication time:
11 / 2006