Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems

Y. Gao (), S. H. Hou () and X. M. Yang ()
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Y. Gao: Chongqing Normal University
S. H. Hou: The Hong Kong Polytechnic University
X. M. Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 1, No 6, 97-120

Abstract: 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.

Keywords: Vector optimization problems; Approximate solutions; ϵ-efficiency; Scalarization; Limiting subdifferentials (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-011-9891-6

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