Approximate optimality and approximate duality in nonsmooth composite vector optimization
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Published:2021-07-15
Issue:3
Volume:37
Page:529-540
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ISSN:1584-2851
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Container-title:Carpathian Journal of Mathematics
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language:
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Short-container-title:CJM
Author:
SIRICHUNWIJIT THANATCHAPORN, ,WANGKEEREE RABIAN,SISARAT NITHIRAT, , ,
Abstract
This paper concentrates on studying a nonsmooth composite vector optimization problem (P for brevity). We employ a fuzzy necessary condition for approximate (weakly) efficient solutions of a nonconvex and nonsmooth cone constrained vector optimization problem established in [Choung, T. D. Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization Ann. Oper. Res. (2020), https://doi.org/10.1007/s10479-020-03740-3.] and the a chain rule for generalized differentiation to provide a necessary condition which exhibited in a Fritz-John type for approximate (weakly) efficient solutions of P. Sufficient optimality conditions for approximate (weakly) efficient solutions to P are also provided by means of proposing the use of (strictly) approximately generalized convex composite vector functions with respect to a cone. Moreover, an approximate dual vector problem to P is given and strong and converse duality assertions for approximate (weakly) efficient solutions are proved.
Publisher
Technical University of Cluj Napoca, North University Center of Baia Mare
Subject
General Mathematics