Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems

Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems

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Article ID: iaor2012254
Volume: 152
Issue: 1
Start Page Number: 97
End Page Number: 120
Publication Date: Jan 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: vector optimization
Abstract:

In this paper, we introduce a new concept of ϵ‐efficiency for vector optimization problems. This extends and unifies various notions of approximate solutions in the literature. Some properties for this new class of approximate solutions are established, and several existence results, as well as nonlinear scalarizations, are obtained by means of the Ekeland’s variational principle. Moreover, under the assumption of generalized subconvex functions, we derive the linear scalarization and the Lagrange multiplier rule for approximate solutions based on the scalarization in Asplund spaces.

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