A general iterative algorithm for finding a common solution of equilibrium and constrained convex minimization problems

2013 ◽  
Vol 43 (4) ◽  
pp. 365-381
Author(s):  
Ming TIAN ◽  
Lei LIU
Keyword(s):  
Iterative Algorithm ◽  
Convex Minimization ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Minimization Problems ◽  
Convex Minimization Problems

New iterative methods for equilibrium and constrained convex minimization problems

2019 ◽  
Vol 12 (03) ◽  
pp. 1950042 ◽  
Author(s):  
Maryam Yazdi
Keyword(s):  
Convex Minimization ◽  
Projection Algorithm ◽  
Averaged Mapping ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Constrained Convex Minimization Problem ◽  
Implicit And Explicit

The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this paper, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative schemes for finding a common solution of an equilibrium problem and a constrained convex minimization problem. Then, we prove some strong convergence theorems which improve and extend some recent results.

scholarly journals A new iterative method for generalized equilibrium and constrained convex minimization problems

2020 ◽  
Vol 74 (2) ◽  
pp. 81
Author(s):  
M. Yazdi
Keyword(s):  
Convex Minimization ◽  
Projection Algorithm ◽  
Strong Convergence Theorem ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Constrained Convex Minimization Problem ◽  
Generalized Equilibrium ◽  
New Iterative Method

The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this paper, we combine the GPA and averaged mapping approach to propose an explicit composite iterative scheme for finding a common solution of a generalized equilibrium problem and a constrained convex minimization problem. Then, we prove a strong convergence theorem which improves and extends some recent results.

scholarly journals A General Iterative Scheme Based on Regularization for Solving Equilibrium and Constrained Convex Minimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Ming Tian
Keyword(s):  
Equilibrium Problem ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Implicit And Explicit ◽  
Split Feasibility

The present paper is divided into two parts. First, we introduce implicit and explicit iterative schemes based on the regularization for solving equilibrium and constrained convex minimization problems. We establish results on the strong convergence of the sequences generated by the proposed schemes to a common solution of minimization and equilibrium problem. Such a point is also a solution of a variational inequality. In the second part, as applications, we apply the algorithm to solve split feasibility problem and equilibrium problem.

scholarly journals A Hybrid Gradient-Projection Algorithm for Averaged Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ming Tian ◽  
Min-Min Li
Keyword(s):  
Hilbert Spaces ◽  
Gradient Projection ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Constrained Convex Minimization ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Averaged Mappings ◽  
General Iterative Method

It is well known that the gradient-projection algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.

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