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Solving stochastic convex feasibility problems in Hilbert spaces

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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

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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},
}