Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets

被引：1

作者：

Luan, Nguyen Ngoc ^{[1
]}

Nam, Nguyen Mau ^{[2
]}

Thieu, Nguyen Nang ^{[3
]}

Yen, Nguyen Dong ^{[3
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math & Informat, 136 Xuan Thuy, Hanoi, Vietnam

[2] Portland State Univ, Fariborz Maseeh Dept Math & Stat, Portland, OR 97207 USA

[3] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2023年 / 199卷 / 02期

基金：

美国国家科学基金会;

关键词：

Convex polyhedron; Generalized convex polyhedron; Separation; Normal cone; Coderivative; Subdifferential; Optimal value function; CONTINUITY; DUALITY;

D O I：

10.1007/s10957-023-02269-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we study some relationships between polyhedral convex sets and generalized polyhedral convex sets. In particular, we clarify by a counterexample that the necessary and sufficient conditions for the separation of a convex set and a polyhedral convex set obtained by Ng et al. (Nonlinear Anal. 55:845-858, 2003; Theorem 3.1) are no longer valid when considering generalized polyhedral convex sets instead of polyhedral convex sets. We also introduce and study the notions of generalized polyhedral multifunctions and optimal value functions generated by generalized polyhedral convex multifunctions along with their generalized differentiation calculus rules.

引用

页码：766 / 786

页数：21

共 20 条

[1] Bonnans JF., 2000, Perturbation analysis of optimization problems, DOI DOI 10.1007/978-1-4612-1394-9
[2] Borwein J.M., 2003, J. Math. Sci. (N. Y.), V115, P2542, DOI DOI 10.1023/A:1022988116044
[3] PARTIALLY FINITE CONVEX-PROGRAMMING .1. QUASI RELATIVE INTERIORS AND DUALITY-THEORY
BORWEIN, JM
LEWIS, AS
[J]. MATHEMATICAL PROGRAMMING, 1992, 57 (01) : 15 - 48
[4] Generalized Differentiation and Duality in Infinite Dimensions under Polyhedral Convexity
Cuong, D. V.
Mordukhovich, B. S.
Nam, N. M.
Sandine, G.
[J]. SET-VALUED AND VARIATIONAL ANALYSIS, 2022, 30 (04) : 1503 - 1526
[5] Hiriart-Urruty Jean-Baptiste., 1993, Convex Analysis and Minimization Algorithms I, Fundamentals, VI., DOI DOI 10.1007/978-3-662-02796-7
[6] Khan A., 2015, SET VALUED OPTIMIZAT, DOI [10.1007/978-3-642-54265-7, DOI 10.1007/978-3-642-54265-7]
[7] Mordukhovich B.S., 2022, CONVEX ANAL, V1
[8] Mordukhovich BS., 2006, VARIATIONAL ANAL GEN, DOI 10.1007/3-540-31246-3
[9] Mordukhovich BS., 2023, EASY PATH CONVEX ANA, DOI [10.1007/978-3-031-26458-0, DOI 10.1007/978-3-031-26458-0]
[10] Fenchel duality in infinite-dimensional setting and its applications
Ng, KF
Song, W
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 55 (7-8) : 845 - 858

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