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Vietnam Journal of Mathematics 40:2&3(2012) 131-163

 

To Dual-Space Theory of Set-Valued

Optimization

Truong Q. Bao1 and Boris S. Mordukhovich2

1Department of Mathematics & Computer Science,

Northern Michigan University, Marquette, Michigan 49855, USA

2Department of Mathematics, Wayne State University,

Detroit, Michigan 48202, USA

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received November 17, 2011

Revised April 30, 2012

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.

2000 Mathematics Subject Classification. 90C29, 90C46, 49J53, 54C60.

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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