Revisiting the Hahn-Banach theorem and nonlinear infinite programming

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Montiel Lopez, P.¹  Ruiz Galan, M.² 

[1] Univ Granada, Dept Sci, Ctr Estudios Superiores Inmaculada, C Toaguina Eguaras 144, Granada 18018, Spain

[2] Univ Granada, Dept Appl Math, ETS Ingn Edificac, C Severo Ochoa S-N, E-18071 Granada, Spain

关键词: Hahn-Banach theorem;    Nonlinear programming;    Lagrange multipliers;    Karush-Kuhn-Tucker theorem;    Fritz John theorem;    Infsup-convexity;   

DOI  :  10.1016/j.jmaa.2017.06.007

来源: Elsevier

【 摘 要 】

The aim of this paper is to state a sharp version of the Konig supremum theorem, an equivalent reformulation of the Hahn-Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free