Pointwise well-posedness in set optimization with cone proper sets

被引：78

作者：

Gutierrez, C. ^{[2
]}

Miglierina, E. ^{[3
]}

Molho, E. ^{[4
]}

Novo, V. ^{[1
]}

机构：

[1] Univ Nacl Educ Distancia, Dept Matemat Aplicada, ETSI Ind, E-28040 Madrid, Spain

[2] Univ Valladolid, Dept Matemat Aplicada, ETS Ingn Telecomunicac, E-47011 Valladolid, Spain

[3] Univ Insubria, Dipartimento Econ, I-21100 Varese, Italy

[4] Univ Pavia, Dipartimento Econ Polit & Metodi Quantitat, I-27100 Pavia, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 04期

关键词：

Set optimization; Well-posedness; Strict minimizer; Scalarization; Gerstewitz's map; Cone proper set; Quasiconvex set-valued map; EKELAND VARIATIONAL PRINCIPLE; VECTOR OPTIMIZATION; VALUED MAPS; THEOREMS; SCALARIZATION; CONVEXITY; EXISTENCE;

D O I：

10.1016/j.na.2011.09.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the well-posedness property in the setting of set optimization problems. By using a notion of well-posed set optimization problem due to Zhang et al. (2009) [18] and a scalarization process, we characterize this property through the well-posedness, in the Tykhonov sense, of a family of scalar optimization problems and we show that certain quasiconvex set optimization problems are well-posed. Our approach is based just on a weak boundedness assumption, called cone properness, that is unavoidable to obtain a meaningful set optimization problem. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1822 / 1833

页数：12

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