Using variational analysis, we study the vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In terms of the coderivatives and normal cones, we present Ferma...
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Using variational analysis, we study the vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In terms of the coderivatives and normal cones, we present Fermat's rules as necessary or sufficient conditions for a super efficient solution of the above problems. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, we study constrained multiobjective optimization problems with objectives being closed-graph multifunctions in Banach spaces. In terms of the coderivatives and Clarke's normal cones, we establish La...
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In this paper, we study constrained multiobjective optimization problems with objectives being closed-graph multifunctions in Banach spaces. In terms of the coderivatives and Clarke's normal cones, we establish Lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions of the above problems. (C) 2007 Elsevier Inc. All rights reserved.
Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the n...
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Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the normal cones, and thereby we provide some characterizations for convex generalized equations to have the metric subregularity. As applications, we establish formulas of the modulus of calmness and provide several characterizations of the calmness. Extending the classical concept of extreme boundary, we introduce a notion of recession cores of closed convex sets. Using this concept, we establish global metric subregularity ( i. e., error bound) results for generalized equations.
We study general constrained multiobjective optimization problems with objectives being closed multifunctions in Banach spaces. In terms of the coderivatives and normal cones, we provide generalized Lagrange multiplie...
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We study general constrained multiobjective optimization problems with objectives being closed multifunctions in Banach spaces. In terms of the coderivatives and normal cones, we provide generalized Lagrange multiplier rules as necessary optimality conditions of the above problems. In an Asplund space setting, sharper results are presented.
We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some...
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We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.
The fuzzy intersection rule for Frechet normal cones in Asplund spaces was established by Mordukhovich and the author using the extremal principle, which appears more convenient to apply in some applications. In this ...
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The fuzzy intersection rule for Frechet normal cones in Asplund spaces was established by Mordukhovich and the author using the extremal principle, which appears more convenient to apply in some applications. In this paper, we present a complete discussion of this rule in various aspects. We show that the fuzzy intersection rule is another characterization of the Asplund property of the space. Various applications are considered as well. In particular, a complete set of fuzzy calculus rules for general lower semicontinuous functions are established. (c) 2005 Elsevier Inc. All rights reserved.
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