Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives

Authors:
Nguyen Le Anh;Phan Quoc Khanh
Affiliations:
Department of Mathematics, University of Science of Hochiminh City, Hochiminh City, Vietnam;Department of Mathematics, International University of Hochiminh City, Hochiminh City, Vietnam
Venue:
Journal of Global Optimization
Year:
2013

Citing 4
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Abstract

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.