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Vietnam Journal of Mathematics 40:2&3(2012)
131-163
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To Dual-Space Theory of Set-Valued
Optimization
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Truong Q. Bao1 and Boris S.
Mordukhovich2
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1Department
of Mathematics & Computer Science,
Northern Michigan University, Marquette,
Michigan 49855, USA
2Department
of Mathematics, Wayne State University,
Detroit,
Michigan 48202, USA
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received November 17,
2011
Revised April 30, 2012
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Abstract. The primary goal of this paper is to
review and further develop the dualspace approach to multiobjective
optimization, focusing mainly on problems with setvalued objectives. This
approach is based on employing advanced tools of variational analysis and generalized
differentiation defined in duals to Banach spaces. Developing this
approach, we present new and updated results on existence of Pareto-type
optimal solutions, necessary optimality and suboptimality conditions, and
also sufficient conditions for global optimality that have never been
considered in the literature in such a generality.
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2000 Mathematics
Subject Classification. 90C29, 90C46, 49J53, 54C60.
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Keywords. Variational analysis, variational and
extremal principles, coderivatives and subdifferentials of set-valued
mappings, generalized Pareto optimality, existence of optimal solutions,
Palais-Smale condition, necessary optimality conditions, sufficient
optimality conditions.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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