A multi step inertial algorithm for approximating a common solution of split generalized mixed equilibrium and minimization problems

2021 ◽  
Author(s):  
Olawale Kazeem Oyewole ◽  
Kazeem Olalekan Aremu ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Common Solution ◽  
Minimization Problems ◽  
Inertial Algorithm ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

scholarly journals Hybrid Algorithms for Minimization Problems over the Solutions of Generalized Mixed Equilibrium and Variational Inclusion Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Real Hilbert Space ◽  
Monotone Mapping ◽  
Variational Inclusion ◽  
Generalized Mixed Equilibrium Problem ◽  
Common Element ◽  
Inclusion Problems ◽  
Minimization Problems ◽  
Inverse Strongly Monotone ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We introduce a new general hybrid iterative algorithm for finding a common element of the set of solution of fixed point for a nonexpansive mapping, the set of solution of generalized mixed equilibrium problem, and the set of solution of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Yao and Liou (2010), Tan and Chang (2011), and other authors.

scholarly journals A Unified Algorithm for Solving Split Generalized Mixed Equilibrium Problem, and for Finding Fixed Point of Nonspreading Mapping in Hilbert Spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 211-232 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Kazeem Olawale Oyewole ◽  
Chibueze Christian Okeke ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Common Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

Abstract The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces.We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.

scholarly journals Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Abdul Rahim Khan ◽  
Chinedu Izuchukwu ◽  
Maggie Aphane ◽  
Godwin Chidi Ugwunnadi
Keyword(s):  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Point Problem ◽  
Numerical Illustration ◽  
Common Solution ◽  
Inertial Algorithm ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
First Time

<p style='text-indent:20px;'>The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.</p>

scholarly journals Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-22
Author(s):  
Lu-Chuan Ceng ◽  
Chi-Ming Chen ◽  
Chin-Tzong Pang
Keyword(s):  
Optimization Problems ◽  
Real Hilbert Space ◽  
Maximal Monotone ◽  
Generalized Mixed Equilibrium Problem ◽  
Monotone Mappings ◽  
Point Problem ◽  
Variational Inclusions ◽  
Common Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem.

scholarly journals Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-26
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Hilbert Space ◽  
Gradient Projection ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Constrained Convex Minimization ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems in a real Hilbert space. It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space.

scholarly journals Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Rabian Wangkeeree ◽  
Hossein Dehghan ◽  
Pakkapon Preechasilp
Keyword(s):  
Strong Convergence ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Generalized Mixed Equilibrium Problem ◽  
Mixed Equilibrium Problem ◽  
Asymptotically Nonexpansive ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.

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