Stochastic approximation results for variational inequality problem using random-type iterative schemes

ABSTRACT

Real world problems are embedded with uncertainties. Therefore, to tackle these problems, one must consider probabilistic nature of the problems both in modeling and solution. In this work, concepts of convergence of the solution of variational inequality in classical functional analysis are extended to a stochastic domain for a random Mann-type iterative and Ishikawa-type iterative schemes in a Banach space. A mean square convergence result is proved for this extension.

KEYWORDS:

• variational inequality problem
• random iterative scheme
• Banach space
• convergence.

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H09
• 54H25
• 58J65

Acknowledgments

The author wishes to thank the anonymous referees for their comments.