G.Wanka : Multiobjective Control-Approximation Problems - Duality and Optimality

Author(s) :

G.Wanka

Title :

Multiobjective Control-Approximation Problems - Duality and Optimality

Electronic source:

application/pdf

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 97-24, 1997

Mathematics Subject Classification :

90C29 [ Multi-objective programming, etc. ]

49N15 [ Duality theory (optimization) ]

41A65 [ Abstract approximation theory ]

41A29 [ Approximation with constraints ]

Abstract :

A general convex multiobjective control-approximation problem is considered with respect to duality. The single objectives contain linear functionals and powers of norms as parts, measuring the distance between the control and the state variables. Moreover, linear inequality restrictions are included. A dual problem is established and weak and strong duality properties as well as necessary and sufficient optimality conditions are derived. So-called point-objective location problems and linear vector optimization problems turn out to be special cases of the investigated problem. Therefore the well-known duality results for linear vector optimization are obtained as special case.

Keywords :

Multiobjective optimization, control-approximation problem, point-objective location, duality, optimality conditions

Language :

english

Publication time :

11/1997