On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality

Takashi Maeda ()
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Takashi Maeda: Kanazawa University

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 2, No 1, 263-279

Abstract: Abstract In this paper, we consider constrained optimization problems with set-valued objective maps. First, we define three types of quasi orderings on the set of all non-empty subsets of n-dimensional Euclidean space. Second, by using these quasi orderings, we define the concepts of lower semi-continuity for set-valued maps and investigate their properties. Finally, based on these results, we define the concepts of optimal solutions to constrained optimization problems with set-valued objective maps and we give some conditions under which these optimal solutions exist to the problems and give necessary and sufficient conditions for optimality.

Keywords: Quasi ordering; Set-valued map; Lower semi-continuous; Pareto optimal solution; Semi-weak Pareto optimal solution; Weak Pareto optimal solution; Subdifferential (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-011-9952-x

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