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.

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 Variant Gradient Projection Methods for the Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Strong Convergence ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Projection Algorithms ◽  
Infinite Dimensional ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Gradient Projection Methods

The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu’s work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed.

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.

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