OPTIMALITY CONDITIONS FOR APPROXIMATE SOLUTIONS OF SET-VALUED OPTIMIZATION PROBLEMS IN REAL LINEAR SPACES

OPTIMALITY CONDITIONS FOR APPROXIMATE SOLUTIONS OF SET-VALUED OPTIMIZATION PROBLEMS IN REAL LINEAR SPACES

E. Kiyani, S. M. Vaezpour, C. J. Tavakoli

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Abstract

In this paper, we deal with optimization problems without assuming any topology. We study approximate eciency and Q- Henig proper eciency for the setvalued vector optimization problems, where Q is not necessarily convex. We use scalarization approaches based on nonconvex separation function to present some necessary and sucient conditions for approximate (proper and weak) ecient solutions.

Keywords

Keywords: Vector optimization, Set-valued maps, Approximate weak eciency, Approximate proper eciency, Vector closure.