Results 21 to 30 of about 948 (198)

Extragradient Method in Optimization: Convergence and Complexity [PDF]

Journal of Optimization Theory and Applications, 2017
We consider the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under the Kurdyka-Lojasiewicz assumption, we prove that the sequence produced by the extragradient method converges to a critical point of the problem and has finite length.
Trong Phong Nguyen, Edouard Pauwels, Emile Richard, Bruce W. Suter   +3 more
openaire   +4 more sources

Extragradient method for convex minimization problem [PDF]

Journal of Inequalities and Applications, 2014
Abstract In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich’s extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann’s iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional ...
Ceng, Lu-Chuan, Liou, Yeong-Cheng, Wen, Ching-Feng   +2 more
openaire   +4 more sources

Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz‐type bifunction. The method is built around two computing phases of a proximal‐like mapping with inertial terms.
Chainarong Khunpanuk, Nuttapol Pakkaranang, Bancha Panyanak, Cristian Chifu   +3 more
wiley   +1 more source

Two New Weak Convergence Algorithms for Solving Bilevel Pseudomonotone Equilibrium Problem in Hilbert Space

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this paper, we introduce two new subgradient extragradient algorithms to find the solution of a bilevel equilibrium problem in which the pseudomonotone and Lipschitz‐type continuous bifunctions are involved in a real Hilbert space. The first method needs the prior knowledge of the Lipschitz constants of the bifunctions while the second method uses a
Gaobo Li, Sun Young Cho
wiley   +1 more source

Convergence Analysis of a Modified Forward‐Backward Splitting Algorithm for Minimization and Application to Image Recovery

Computational and Mathematical Methods, Volume 2022, Issue 1, 2022., 2022
Many applications in applied sciences and engineering can be considered as the convex minimization problem with the sum of two functions. One of the most popular techniques to solve this problem is the forward‐backward algorithm. In this work, we aim to present a new version of splitting algorithms by adapting with Tseng’s extragradient method and ...
Kunrada Kankam, Watcharaporn Cholamjiak, Prasit Cholamjiak, Naeem Jan   +3 more
wiley   +1 more source

Extragradient Methods for Solving Split Feasibility Problem and General Equilibrium Problem and Resolvent Operators in Banach Spaces

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we introduce a new extragradient algorithm by using generalized metric projection. We prove a strong convergence theorem for finding a common element of the solution set of split feasibility problem and the set of fixed points of relatively nonexpansive mapping and a finite family of resolvent operator and the set of solutions of an ...
Mostafa Ghadampour, Giovanni Di Fratta
wiley   +1 more source

A Forward‐Backward‐Forward Algorithm for Solving Quasimonotone Variational Inequalities

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we continue to investigate the convergence analysis of Tseng‐type forward‐backward‐forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self‐adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators.
Tzu-Chien Yin, Nawab Hussain, Calogero Vetro   +2 more
wiley   +1 more source

Novel Algorithms for Solving a System of Absolute Value Variational Inequalities

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The goal of this paper is to study a new system of a class of variational inequalities termed as absolute value variational inequalities. Absolute value variational inequalities present a rational, pragmatic, and novel framework for investigating a wide range of equilibrium problems that arise in a variety of disciplines.
Safeera Batool, Muhammad Aslam Noor, Riaz Ahmad, Ilyas Khan, Mulugeta Andualem, Andrea Scapellato   +5 more
wiley   +1 more source

An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications

Axioms, 2020
Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the ...
Nopparat Wairojjana, Habib ur Rehman, Ioannis K. Argyros, Nuttapol Pakkaranang   +3 more
doaj   +1 more source

An Iterative Algorithm for Solving Fixed Point Problems and Quasimonotone Variational Inequalities

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this paper, we survey a common problem of the fixed point problem and the quasimonotone variational inequality problem in Hilbert spaces. We suggest an iterative algorithm for finding a common element of the solution of a quasimonotone variational inequality and the fixed point of a pseudocontractive operator.
Tzu-Chien Yin, Yan-Kuen Wu, Ching-Feng Wen, Ljubisa Kocinac   +3 more
wiley   +1 more source