Solution Continuity and Gap Functions with Error Bounds for Vector Equilibrium Problems under Improvement Sets via Scalarization

CHEN Juan; CHEN Chunrong

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Solution Continuity and Gap Functions with Error Bounds for Vector Equilibrium Problems under Improvement Sets via Scalarization

CHEN Juan,CHEN Chunrong *

College of Mathematics and Statistics, Chongqing University, Chongqing 401331

*Correspondence author

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Funding: National Natural Science Foundation of China （No.11301567）

Opened online:17 January 2020

Accepted by: none

Citation: CHEN Juan,CHEN Chunrong.Solution Continuity and Gap Functions with Error Bounds for Vector Equilibrium Problems under Improvement Sets via Scalarization[OL]. [17 January 2020] http://en.paper.edu.cn/en_releasepaper/content/4750369

In this paper, firstly, we discuss useful linear scalarization characterizations to solutions for unified vector equilibrium problems via improvement sets. Then, using scalarization methods and main assumptions of generalized convexity and monotonicity, the solution continuity for parametric unified vector equilibrium problems, (regularized) gap functions and error bounds, and gap functions via the minimax strategy for unified vector equilibrium problems under improvement sets are investigated, respectively. Our results generalize or improve related ones in the literature. Especially, the results obtained on (regularized) gap functions and error bounds are general and new.

Keywords:Vector equilibrium problems; Solution continuity; Gap functions; Error bounds; Improvement set; Scalarization

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