Gap Functions and Error Bounds for Weak Generalized Ky Fan Inequalities. (19th May 2018)

• Record Type: Journal Article
• Authors: Li, G. H.; Li, S. J.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 7(2018)
• Page Start: 763
• Page End: 783
• Publication Date: 2018-05-19
• Subjects: Error bound -- gap function -- image space analysis -- regular weak separation function -- weak generalized Ky Fan inequality; 49J40 -- 90C48; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1421222
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we study a weak generalized Ky Fan inequality with cone constraints through image space analysis. First, we characterize the separation for the weak generalized Ky Fan inequality with cone constraints using the saddle points of generalized Lagrangian function. Then, we use regular weak separation functions to construct gap functions and regularized gap functions for the weak generalized Ky Fan inequality with cone constraints in a general way, and establish its error bounds in terms of these gap functions.