SUBDIFFERENTIAL CALCULUS FOR ORDERED MULTIFUNCTIONS WITH APPLICATIONS TO SET-VALUED OPTIMIZATION

被引：0

作者：

Mordukhovich B.S. ^{[1
]}

Nguyen O. ^{[1
]}

机构：

[1] Department of Mathematics, Wayne State University, Detroit, 48202, MI

来源：

Journal of Applied and Numerical Optimization | 2023年 / 5卷 / 01期

关键词：

Coderivatives; Existence of optimal solutions; Relative Pareto minimizers; Subdifferential Palais-Smale condition; Variational analysis;

D O I：

10.23952/jano.5.2023.1.03

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses the study of subdifferentials for set-valued mappings/multifunctions, which take values in ordered spaces. First we obtain the main calculus (sum and chain) rules for such subdifferentials. Then the developed subdifferential calculus is applied to establishing existence theorems for the so-called relative Pareto minimizers in general problems of set-valued optimization with constraints of various types. © 2023 Journal of Applied and Numerical Optimization.

引用

页码：27 / 53

页数：26

共 10 条

[1]

Khan A. A., Tammer C., Zalinescu C., Set-Valued Optimization. An Introduction with Applications, (2015)

[2]

Tammer C., Weidner P., Scalarization and Separation by Translation Invariant Functions, (2020)

[3]

Mordukhovich B. S., Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications, (2006)

[4]

Mordukhovich B. S., Variational Analysis and Applications, (2018)

[5]

Rockafellar R. T., Wets R. J-B., Variational Analysis, (1998)

[6]

Bao T. Q., Mordukhovich B. S., Variational principles for set-valued mappings with applications to multiobjective optimization, Control Cybern, 36, pp. 531-562, (2007)

[7]

Bao T. Q., Mordukhovich B. S., Relative Pareto minimizers for multiobjective problems: existence and optimality conditions, Math. Program, 122, pp. 301-347, (2010)

[8]

Mordukhovich B. S., Complete characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions, Trans. Amer. Math. Soc, 340, pp. 1-35, (1993)

[9]

Mordukhovich B. S., Nam N. M., Convex Analysis and Beyond, I: Basic Theory, (2022)

[10]

Kim D.S., Mordukhovich B. S., Pham T.-S., Tuyen N. V., Existence of efficient and properly efficient solutions to problems of constrained vector optimization, Math. Program, 190, pp. 259-283, (2021)

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