# Approximate quasi efficiency of set-valued optimization problems via weak subdifferential

Approximate quasi efficiency of set-valued optimization problems via weak subdifferential This paper deals with the approximate quasi efficient solutions of set-valued optimization problems. We establish the necessary and sufficient optimality conditions for $$\epsilon e$$ ϵ e -quasi efficiency via weak subdifferential under some approximate cone convexity assumptions. We also study duality results of Wolfe and Mond-Weir types for Geoffrion $$\epsilon e$$ ϵ e -quasi efficiency of finite dimensional set-valued optimization problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

# Approximate quasi efficiency of set-valued optimization problems via weak subdifferential

, Volume 74 (4) – Nov 9, 2016
20 pages
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Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0099-4
Publisher site
See Article on Publisher Site

### Abstract

This paper deals with the approximate quasi efficient solutions of set-valued optimization problems. We establish the necessary and sufficient optimality conditions for $$\epsilon e$$ ϵ e -quasi efficiency via weak subdifferential under some approximate cone convexity assumptions. We also study duality results of Wolfe and Mond-Weir types for Geoffrion $$\epsilon e$$ ϵ e -quasi efficiency of finite dimensional set-valued optimization problems.

### Journal

SeMA JournalSpringer Journals

Published: Nov 9, 2016

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