NONCONVEX SEPARATION FUNCTIONAL IN LINEAR SPACES WITH APPLICATIONS TO VECTOR EQUILIBRIA

被引：43

作者：

Gutierrez, Cesar ^{[1
]}

Novo, Vicente ^{[2
]}

Luis Rodenas-Pedregosa, Juan ^{[2
]}

Tanaka, Tamaki ^{[3
]}

机构：

[1] Univ Valladolid, ETS Ingn Telecomun, Dept Matemat Aplicada, Paseo Belen 15,Campus Miguel Delibes, E-47011 Valladolid, Spain

[2] UNED, Dept Matemat Aplicada, ETSI Ind, C Juan Rosal 12,Ciudad Univ, Madrid 28040, Spain

[3] Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan

来源：

SIAM JOURNAL ON OPTIMIZATION | 2016年 / 26卷 / 04期

关键词：

nonlinear scalarization functional; algebraic interior; vector closure; vector equilibrium problem; SET-VALUED OPTIMIZATION; PROPER EFFICIENCY; VARIATIONAL PRINCIPLE; OPTIMALITY CONDITIONS; ALGEBRAIC INTERIOR; SCALARIZATION; MAPS; WEAK;

D O I：

10.1137/16M1063575

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the so-called nonconvex separation functional is studied in a real linear space not necessarily endowed with a topology. The essential properties of this functional, which are well known in the topological framework, are derived by using algebraic counterparts to the topological concepts of interior and closure. Finally, it is used to characterize, in the same algebraic setting and by scalarization, weak efficient solutions of vector equilibrium problems defined through algebraic solid ordering sets.

引用

页码：2677 / 2695

页数：19

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