Generalized -D-gap functions and error bounds for a class of equilibrium problems

Abstract

In this paper, we introduce and study the generalized -D-gap function for an equilibrium problem. We give sufficient conditions under which a critical point of the generalized -D-gap function is a solution of the equilibrium problem, and develop a descent scheme for locating these critical points. Using the generalized -D-gap function, we construct an error bound for the equilibrium problem. We support our approach with concrete examples.

Keywords:

• Generalized -D-gap function
• equilibrium problem
• -strongly monotone
• -strongly convex
• error bound
• monotone operator
• projection operator

AMS Subject Classifications:

• 49J30
• 49J40
• 47J25
• 47H09

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

L.-C. Ceng is supported by the Innovation Program of Shanghai Municipal Education Commission [grant number 15ZZ068]; PhD Program Foundation of Ministry of Education of China [grant number 20123127110002]; Program for Outstanding Academic Leaders in Shanghai City [grant number 15XD1503100]; C.-F. Wen and N.-C. Wong are supported by the Taiwan MOST [grant number 105-2115-M-037-001], [grant number 104-2115-M-110-009-MY2], respectively, as well as the NSYSU-KMU Joint Research Project [garnt number NSYSUKMU 106-P014].