A stochastic iteration method for the solution of finite dimensional variational inequalities

Abstract

Let A be a real n x n matrix, let b a real column n-vector and φ: Rⁿ → R such that Ax + δφ(x) ∋b where δφ is the sub gradient of φ. A computable stochastic iterative scheme is suggested; which is a modification of Robbins-Monroe procedure and studied in the context of the above concrete problem. This scheme is shown to converge strongly to the solution of the above problem.

Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 301-304