A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces

1986 ◽  
pp. 28-47 ◽  
Author(s):  
James P. Boyle ◽  
Richard L. Dykstra
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets

scholarly journals ON SOME GENERALIZATION OF SMOOTHING PROBLEMS

2015 ◽  
Vol 20 (3) ◽  
pp. 311-328 ◽  
Author(s):  
Svetlana Asmuss ◽  
Natalja Budkina
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets ◽  
Special Cases

The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.

scholarly journals Finding best approximation pairs relative to two closed convex sets in Hilbert spaces

2004 ◽  
Vol 127 (2) ◽  
pp. 178-192 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Patrick L. Combettes ◽  
D.Russell Luke
Keyword(s):  
Hilbert Spaces ◽  
Best Approximation ◽  
Convex Sets

scholarly journals On angles between convex sets in Hilbert spaces

2021 ◽  
Vol 502 (1) ◽  
pp. 125239
Author(s):  
Heinz H. Bauschke ◽  
Hui Ouyang ◽  
Xianfu Wang
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets

scholarly journals Approximating solutions of generalized pseudocontractive variational inequalities by admissible perturbation type iterative methods

2013 ◽  
Vol 22 (2) ◽  
pp. 237-241
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Variational Inequalities ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convex Sets ◽  
Perturbation Operator ◽  
Strongly Nonlinear ◽  
Admissible Perturbation

In this paper we give the solvability class of generalized strongly nonlinear variational inequalities modified by the use of the new concept of admissible perturbation operator on nonempty closed convex sets in Hilbert spaces.

scholarly journals Computing infima on convex sets, with applications in Hilbert spaces

2004 ◽  
Vol 132 (9) ◽  
pp. 2723-2732
Author(s):  
Douglas Bridges ◽  
Hajime Ishihara ◽  
Luminiţa Vîţă
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets

scholarly journals Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 119
Author(s):  
Xinglong Wang ◽  
Jing Zhao ◽  
Dingfang Hou
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets ◽  
Iterative Algorithms ◽  
Intensity Modulated Radiation Therapy ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Cq Algorithm ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

scholarly journals Convex sets strict separation in Hilbert spaces

2014 ◽  
Vol 8 ◽  
pp. 3155-3160
Author(s):  
M. A. M. Ferreira ◽  
J. A. Filipe
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets
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