TY - CHAP

T1 - The outer bregman projection method for stochastic feasibility problems in banach spaces

AU - Butnariu, Dan

AU - Resmerita, Elena

PY - 2001

Y1 - 2001

N2 - We present an iterative method for solving, eventually infinite systems of inequalities g(ω, x)≤0, a.e. (Ω), in which the functions g(ω,·) are defined, convex, lower semicontinuous and essentially uniformly bounded on a Banach space. We show that the proposed method produces sequences which accumulate weakly to solutions of the system, provided that such solutions exist. In the most usual Banach spaces, the size of the constraint violations along the sequences generated by the iterative procedure converges in mean to zero. We prove that this method can be implemented for solving consistent operator equations (like first kind Fredholm or Volterra equations, some potential equations, etc.) when they have solutions in Hilbert, Lebesgue or Sobolev spaces.

AB - We present an iterative method for solving, eventually infinite systems of inequalities g(ω, x)≤0, a.e. (Ω), in which the functions g(ω,·) are defined, convex, lower semicontinuous and essentially uniformly bounded on a Banach space. We show that the proposed method produces sequences which accumulate weakly to solutions of the system, provided that such solutions exist. In the most usual Banach spaces, the size of the constraint violations along the sequences generated by the iterative procedure converges in mean to zero. We prove that this method can be implemented for solving consistent operator equations (like first kind Fredholm or Volterra equations, some potential equations, etc.) when they have solutions in Hilbert, Lebesgue or Sobolev spaces.

UR - http://www.scopus.com/inward/record.url?scp=77956972456&partnerID=8YFLogxK

U2 - 10.1016/S1570-579X(01)80007-0

DO - 10.1016/S1570-579X(01)80007-0

M3 - Chapter

AN - SCOPUS:77956972456

T3 - Studies in Computational Mathematics

SP - 69

EP - 86

BT - Studies in Computational Mathematics

PB - Elsevier

ER -