# 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

- Chicago
- Crombez, Gilbert. 1996. “Solving Stochastic Convex Feasibility Problems in Hilbert Spaces.”
*Numerical Functional Analysis and Optimization*17 (9-10): 877–892. - APA
- 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.
- MLA
- Crombez, Gilbert. “Solving Stochastic Convex Feasibility Problems in Hilbert Spaces.”
*NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION*17.9-10 (1996): 877–892. Print.

@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}, keyword = {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}, }