Solving stochastic convex feasibility problems in Hilbert spaces
- Author
- Gilbert Crombez
- Organization
- Abstract
- In a stochastic convex feasibility problem connected with a complete probability space (Omega, A, mu) and a family of closed convex sets {C-omega}(omega is an element of Omega) in a real Hilbert space H, one wants to find a point that belongs to C-omega for mu-almost all omega is an element of Omega. We present a projection-based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a mu-almost common point. We then give a general condition assuring norm convergence of this sequence to that mu-almost common point.
- Keywords
- PROJECTION METHODS, CONVERGENCE, almost common point, expected-projection methods, stochastic convex feasibility problems
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-181226
- MLA
- Crombez, Gilbert. “Solving Stochastic Convex Feasibility Problems in Hilbert Spaces.” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol. 17, no. 9–10, 1996, pp. 877–92.
- APA
- Crombez, G. (1996). Solving stochastic convex feasibility problems in Hilbert spaces. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 17(9–10), 877–892.
- Chicago author-date
- Crombez, Gilbert. 1996. “Solving Stochastic Convex Feasibility Problems in Hilbert Spaces.” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 17 (9–10): 877–92.
- Chicago author-date (all authors)
- Crombez, Gilbert. 1996. “Solving Stochastic Convex Feasibility Problems in Hilbert Spaces.” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 17 (9–10): 877–892.
- Vancouver
- 1.Crombez G. Solving stochastic convex feasibility problems in Hilbert spaces. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. 1996;17(9–10):877–92.
- IEEE
- [1]G. Crombez, “Solving stochastic convex feasibility problems in Hilbert spaces,” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol. 17, no. 9–10, pp. 877–892, 1996.
@article{181226,
abstract = {{In a stochastic convex feasibility problem connected with a complete probability space (Omega, A, mu) and a family of closed convex sets {C-omega}(omega is an element of Omega) in a real Hilbert space H, one wants to find a point that belongs to C-omega for mu-almost all omega is an element of Omega. We present a projection-based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a mu-almost common point. We then give a general condition assuring norm convergence of this sequence to that mu-almost common point.}},
author = {{Crombez, Gilbert}},
issn = {{0163-0563}},
journal = {{NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION}},
keywords = {{PROJECTION METHODS,CONVERGENCE,almost common point,expected-projection methods,stochastic convex feasibility problems}},
language = {{eng}},
number = {{9-10}},
pages = {{877--892}},
title = {{Solving stochastic convex feasibility problems in Hilbert spaces}},
volume = {{17}},
year = {{1996}},
}