Auxiliary Principle Technique for Hierarchical Equilibrium Problems

Pham Ngoc Anh () and Qamrul Hasan Ansari ()
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Pham Ngoc Anh: Posts and Telecommunications Institute of Technology
Qamrul Hasan Ansari: Aligarh Muslim University

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 3, No 13, 882-912

Abstract: Abstract In this paper, building upon auxiliary principle technique and using proximal operator, we introduce a new explicit algorithm for solving monotone hierarchical equilibrium problems. The considered problem is a monotone equilibrium problem, where the constraint is the solution set of a set-valued variational inequality problem. The strong convergence of the proposed algorithm is studied under strongly monotone and Lipschitz-type assumptions of the bifunction. By combining with parallel techniques, the convergence result is also established for the equilibrium problem involving a finite system of demicontractive mappings. Several fundamental experiments are provided to illustrate the numerical behavior of the proposed algorithm and comparison with other known algorithms is studied.

Keywords: Equilibrium problems; Lipschitz-type bifunctions; Monotone bifunctions; Auxiliary principle; Generalized variational inequalities; 65K10; 90C25; 49J35; 47J25; 47J20; 91B50 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01814-1

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