Scalar representations and Hausdorff continuity of solution mappings to parametric set optimization problems via set less order relations

被引：0

作者：

Anh, Lam Quoc ^{[1
]}

Duoc, Pham Thanh ^{[2
,3
,4
]}

Linh, Ha Manh ^{[3
,5
]}

机构：

[1] Can Tho Univ, Teacher Coll, Dept Math, Can Tho, Vietnam

[2] Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam

[3] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

[4] Can Tho Univ Technol, Fac Informat Technol, Can Tho, Vietnam

[5] Univ Informat Technol, Dept Math & Phys, Ho Chi Minh City, Vietnam

来源：

OPERATIONS RESEARCH LETTERS | 2024年 / 53卷

关键词：

Approximate solution; Hausdorff continuity; Nonlinear scalarization; Scalar representation; Set optimization problem; Set less order relation; CONNECTEDNESS; STABILITY; CONE;

D O I：

10.1016/j.orl.2024.107071

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：

This paper aims to formulate scalar representations and stability conditions for parametric set optimization problems involving set less order relations. We first introduce new nonlinear scalarization functions for sets and discuss their properties, and then they are utilized to establish scalar representations for solutions to such problems. Finally, we study sufficient conditions for the Hausdorff continuity of approximate solution mappings to the reference problems. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：8

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