非光滑复合向量优化中的近似最优性和近似对偶性

IF 1.4 4区数学 Q1 MATHEMATICS

Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI:10.37193/cjm.2021.03.14

Thanatchaporn Sirichunwijit, R. Wangkeeree, Nithirat Sisarat

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引用次数: 0

摘要

本文主要研究一个非光滑复合向量优化问题（简称P）。我们在[Chung，T.D.中建立了一个非凸和非凸锥约束向量优化问题的近似（弱）有效解的模糊必要条件。非光滑和非凸圆锥约束向量优化中的近似解Ann.Oper.Res.（2020），https://doi.org/10.1007/s10479-020-03740-3.]以及广义微分的链式规则，以提供P的近似（弱）有效解在Fritz-John型中表现出的必要条件。通过提出使用关于锥的（严格）近似广义凸复合向量函数，也提供了P的近似（弱）有效解的充分最优性条件。此外，给出了P的一个近似对偶向量问题，并证明了近似（弱）有效解的强对偶断言和逆对偶断言。

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Approximate optimality and approximate duality in nonsmooth composite vector optimization

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.

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来源期刊

Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.