Lagrange Multipliers for [epsi]-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces

This paper presents some results concerning the existence of the Lagrange multipliers for vector optimization problems in the case where the ordering cone in the codomain has an empty interior. The main tool for deriving our assertions is a scalarization by means of a functional introduced by Hiriar...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2010-04, Vol.145 (1), p.196
Main Authors: Durea, M, Dutta, J, Tammer, C
Format: Article
Language:English
Subjects:
Approximation
Banach spaces
Lagrange multiplier
Mathematical functions
Mathematics
Optimization
Pareto optimum
Studies
Online Access:Get full text
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Summary:This paper presents some results concerning the existence of the Lagrange multipliers for vector optimization problems in the case where the ordering cone in the codomain has an empty interior. The main tool for deriving our assertions is a scalarization by means of a functional introduced by Hiriart-Urruty (Math. Oper. Res. 4:79-97, 1979) (the so-called oriented distance function). Moreover, we explain some applications of our results to a vector equilibrium problem, to a vector control-approximation problem and to an unconstrainted vector fractional programming problem. [PUBLICATION ABSTRACT]
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-009-9609-1