A proximal method for equilibrium problems under growth conditions

2016 ◽  
Vol 28 (5-6) ◽  
pp. 669-676
Author(s):  
Abdellatif Moudafi ◽  
Muhammad Aslam Noor
Keyword(s):  
Equilibrium Problems ◽  
Growth Conditions ◽  
Proximal Method

scholarly journals PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS

2016 ◽  
Vol 21 (4) ◽  
pp. 478-501 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Proximal Methods ◽  
Proximal Method ◽  
Weak And Strong Convergence ◽  
Split Variational Inequality

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

An Inexact Proximal Method with Proximal Distances for Quasimonotone Equilibrium Problems

2017 ◽  
Vol 5 (4) ◽  
pp. 545-561 ◽  
Author(s):  
Lennin Mallma Ramirez ◽  
Erik Alex Papa Quiroz ◽  
P. R. Oliveira
Keyword(s):  
Equilibrium Problems ◽  
Proximal Method ◽  
Inexact Proximal

scholarly journals Two-Step Proximal Method for Equilibrium Problems in Hadamard spaces

2020 ◽  
pp. 71-74
Author(s):  
Yana I. Vedel ◽  
Vladimir V. Semenov ◽  
Kateryna M. Golubeva
Keyword(s):  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Saddle Point Problems ◽  
Proximal Method ◽  
Nash Equilibrium Point ◽  
Special Cases ◽  
Step Algorithm ◽  
Monotone Bifunctions

We propose a novel two-step proximal method for solving equilibrium problems in Hadamard spaces. The equilibrium problem is very general in the sense that it includes as special cases many applied mathematical models such as: variational inequalities, optimization problems, saddle point problems, and Nash equilibrium point problems. The proposed algorithm is the analog of the two-step algorithm for solving the equilibrium problem in Hilbert spaces explored earlier. We prove the weak convergence of the sequence generated by the algorithm for pseudo-monotone bifunctions. Our results extend some known results in the literature for pseudo-monotone equilibrium problems.

scholarly journals ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS

2020 ◽  
pp. 18-30
Author(s):  
Ya. I. Vedel ◽  
S. V. Denisov ◽  
V. V. Semenov
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Proximal Method ◽  
Iterative Regularization ◽  
Inequality Problem ◽  
Lipschitz Continuous ◽  
Convergence Of Sequences ◽  
Continuous Operators ◽  
Monotone Bifunctions

In this paper, we consider bilevel problem: variational inequality problem over the set of solutions the equilibrium problems. To solve this problem, an iterative algorithm is proposed that combines the ideas of a two-stage proximal method and iterative regularization. For monotone bifunctions of Lipschitz type and strongly monotone Lipschitz continuous operators, the theorem on strong convergence of sequences generated by the algorithm is proved.

scholarly journals ABOUT THE TWO-STAGE PROXIMAL METHOD FOR SOLVING OF EQUILIBRIUM PROBLEMS

2019 ◽  
pp. 23-31 ◽  
Author(s):  
Ya. I. Vedel ◽  
V. V. Semenov ◽  
L. M. Chabak
Keyword(s):  
Game Theory ◽  
Hilbert Space ◽  
Approximate Solution ◽  
Mathematical Programming ◽  
Weak Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Proximal Method ◽  
Existence Of A Solution ◽  
Mathematical Programming Problems

In this paper, the weak convergence of an iterative twostage proximal method for the approximate solution of the equilibrium problem in a Hilbert space is investigated. This method was recently been developed by Vedel and Semenov and can be used to solve mathematical programming problems, variational inequalities and game theory problems. The analysis of the convergence of the method was carried out under the assumption of the existence of a solution of the equilibrium problem and under conditions weaker than the previously considered ones.

Influence of MBE Growth Conditions on Dislocation Densities of GaAs/Ge Epilayers Grown on Silicon Substrates

1985 ◽  
Vol 43 ◽  
pp. 364-365
Author(s):  
K.M. Hones ◽  
P. Sheldon ◽  
B.G. Yacobi ◽  
A. Mason
Keyword(s):  
High Efficiency ◽  
Lattice Mismatch ◽  
Low Cost ◽  
Growth Conditions ◽  
Nonradiative Recombination ◽  
Device Structure ◽  
Si Substrates ◽  
Transmission Electron ◽  
Dislocation Densities ◽  
Dislocation Type

There is increasing interest in growing epitaxial GaAs on Si substrates. Such a device structure would allow low-cost substrates to be used for high-efficiency cascade- junction solar cells. However, high-defect densities may result from the large lattice mismatch (∼4%) between the GaAs epilayer and the silicon substrate. These defects can act as nonradiative recombination centers that can degrade the optical and electrical properties of the epitaxially grown GaAs. For this reason, it is important to optimize epilayer growth conditions in order to minimize resulting dislocation densities. The purpose of this paper is to provide an indication of the quality of the epitaxially grown GaAs layers by using transmission electron microscopy (TEM) to examine dislocation type and density as a function of various growth conditions. In this study an intermediate Ge layer was used to avoid nucleation difficulties observed for GaAs growth directly on Si substrates. GaAs/Ge epilayers were grown by molecular beam epitaxy (MBE) on Si substrates in a manner similar to that described previously.

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