A Brezis-Browder principle on partially ordered spaces and related ordering theorems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Flores-Bazan, F.²  Gutierrez, C.¹  Novo, V.³ 

[1] Univ Valladolid, ETSI Informat, Dept Matemat Aplicada, E-47011 Valladolid, Spain

[2] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Concepcion, Chile

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

关键词: Quasi order;    Existence of strong minimal points;    Ordering principle;    Brezis-Browder principle;    Bishop-Phelps lemma;    Ekeland variational principle;    Vector optimization;    Set-valued optimization;    Set solution criterion;    Existence of strong efficient solutions;   

DOI  :  10.1016/j.jmaa.2010.09.014

来源: Elsevier

【 摘 要 】

Through a simple extension of Brezis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free