Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems

A. Iusem () and F. Lara ()
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A. Iusem: Instituto Nacional de Matemática Pura e Aplicada (IMPA)
F. Lara: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 20, 443-461

Abstract: Abstract 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.

Keywords: Proximal point algorithms; Equilibrium problems; Pseudomonotonicity; Quasiconvexity; Strong quasiconvexity (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-021-01951-7

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