Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems

2021 ◽  
Author(s):  
A. Iusem ◽  
F. Lara
Keyword(s):  
Equilibrium Problems ◽  
Proximal Point ◽  
Proximal Point Algorithms

On a Bregman regularized proximal point method for solving equilibrium problems

2019 ◽  
Vol 13 (5) ◽  
pp. 1143-1155
Author(s):  
J. X. Cruz Neto ◽  
P. S. M. Santos ◽  
R. C. M. Silva ◽  
J. C. O. Souza
Keyword(s):  
Equilibrium Problems ◽  
Point Method ◽  
Proximal Point Method ◽  
Proximal Point

scholarly journals Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-31 ◽  
Author(s):  
Kriengsak Wattanawitoon ◽  
Poom Kumam
Keyword(s):  
Equilibrium Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Zero Point ◽  
Monotone Operators ◽  
Common Element ◽  
Proximal Point ◽  
Strong And Weak Convergence ◽  
Mixed Equilibrium Problems ◽  
Inverse Strongly Monotone

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.

scholarly journals On Mixed Equilibrium Problems in Hadamard Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chinedu Izuchukwu ◽  
Kazeem Olalekan Aremu ◽  
Olawale Kazeem Oyewole ◽  
Oluwatosin Temitope Mewomo ◽  
Safeer Hussain Khan
Keyword(s):  
Equilibrium Problem ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Mixed Equilibrium Problem ◽  
Proximal Point ◽  
Unique Existence ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Resolvent Operator

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis

Optimization ◽  
2019 ◽  
Vol 69 (7-8) ◽  
pp. 1655-1680 ◽  
Author(s):  
Nopparat Wairojjana ◽  
Nuttapol Pakkaranang ◽  
Izhar Uddin ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal
Keyword(s):  
Convergence Analysis ◽  
Convex Combination ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Combination Technique ◽  
Minimization Problems
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