Convergence of Solutions of a Set Optimization Problem in the Image Space

被引：29

作者：

Gutierrez, Cesar ^{[1
]}

Miglierina, Enrico ^{[2
]}

Molho, Elena ^{[3
]}

Novo, Vicente ^{[4
]}

机构：

[1] Univ Valladolid, Paseo de Belen 15,Campus Miguel Delibes, E-47011 Valladolid, Spain

[2] Univ Cattolica Sacro Cuore, Via Necchi 9, I-20123 Milan, Italy

[3] Univ Pavia, Via S Felice 5, I-27100 Pavia, Italy

[4] Univ Nacl Educ Distancia, C Juan del Rosal 12,Ciudad Univ, E-28040 Madrid, Spain

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2016年 / 170卷 / 02期

关键词：

Set optimization; Set relations; Minimal solutions; Stability; Set convergence; WELL-POSEDNESS; SCALARIZATION; CONTINUITY; STABILITY; THEOREMS;

D O I：

10.1007/s10957-016-0942-x

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：

The present work is devoted to the study of stability in set optimization. In particular, a sequence of perturbed set optimization problems, with a fixed objective map, is studied under suitable continuity assumptions. A formulation of external and internal stability of the solutions is considered in the image space, in such a way that the convergence of a sequence of solutions of perturbed problems to a solution of the original problem is studied under appropriate compactness assumptions. Our results can also be seen as an extension to the set-valued framework of known stability results in vector optimization.

引用

页码：358 / 371

页数：14

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