Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems

We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective is the sum of a strongly quasiconvex function plus the standard quadratic regularization term for optimization problems. We prove, under sui...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 193; no. 1-3; pp. 443 - 461
Main Authors: Iusem, A., Lara, F.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Convexity
Engineering
Equilibrium
Equilibrium methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Regularization
Theory of Computation
Quasiconvexity
Strong quasiconvexity
Pseudomonotonicity
Proximal point algorithms
Equilibrium problems
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective is the sum of a strongly quasiconvex function plus the standard quadratic regularization term for optimization problems. We prove, under suitable additional assumptions, convergence of the generated sequence to a solution of the equilibrium problem, whenever the bifunction is strongly quasiconvex in its second argument, thus extending the validity of the convergence analysis of proximal point methods for equilibrium problems beyond the standard assumption of convexity of the bifunction in the second argument.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01951-7