scholarly journals AN ITERATIVE METHOD FOR FINITE FAMILY OF HEMI CONTRACTIONS IN HILBERT SPACE

Cubo (Temuco) ◽  
2013 ◽  
Vol 15 (2) ◽  
pp. 105-110
Author(s):  
Balwant Singh Thakur
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Finite Family

scholarly journals A New Iterative Algorithm for Pseudomonotone Equilibrium Problem and a Finite Family of Demicontractive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
F. U. Ogbuisi ◽  
F. O. Isiogugu
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Equilibrium Problem ◽  
Numerical Experiments ◽  
Real Hilbert Space ◽  
Convex Combination ◽  
Convergence Result ◽  
Finite Family ◽  
Demicontractive Mappings ◽  
New Iterative Method

In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method.

scholarly journals Explicit Scheme for Fixed Point Problem for Nonexpansive Semigroup and Split Equilibrium Problem in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Pei Zhou ◽  
Gou-Jie Zhao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Explicit Scheme ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem

We establish an iterative method for finding a common element of the set of fixed points of nonexpansive semigroup and the set of split equilibrium problems. Under suitable conditions, some strong convergence theorems are proved. Our works improve previous results for nonexpansive semigroup.

scholarly journals A New Iterative Method for Equilibrium Problems and Fixed Point Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Abdul Latif ◽  
Mohammad Eslamian
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Common Element ◽  
Continuous Mappings ◽  
New Iterative Method

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.

Projection algorithms for composite minimization

2017 ◽  
Vol 33 (3) ◽  
pp. 389-397
Author(s):  
XIAONAN YANG ◽  
◽  
HONG-KUN XU ◽  
Keyword(s):  
Hilbert Space ◽  
Minimization Problem ◽  
Convex Functions ◽  
Gradient Descent ◽  
Optimal Solution ◽  
Finite Family ◽  
Local Function ◽  
Projection Algorithms ◽  
Local Functions ◽  
Convex Subsets

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms consist of two steps. Once the kth iterate is constructed, an inner circle of gradient descent process is executed through each local function, and then a parallel or cyclic projection process is applied to produce the (k + 1) iterate. These algorithms are proved to converge to an optimal solution of the composite minimization problem under investigation upon assuming boundedness of the gradients at the iterates of the local functions and the stepsizes being chosen appropriately.

An effective iterative method to build the Naimark extension of rank-n POVMs

2017 ◽  
Vol 15 (04) ◽  
pp. 1750029 ◽  
Author(s):  
Nicola Dalla Pozza ◽  
Matteo G. A. Paris
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Projective Measurement ◽  
Probability Operator

We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the projective measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.

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