Convergence Analysis of Gauss-Type Proximal Point Method for Variational Inequalities
[1]
Mohammed Harunor Rashid , Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh.
In the present paper, we introduce a Gauss-type proximal point algorithm for solving the variational inequality problem, that is, a problem involving functional acting between Banach space and its dual space, which has to be solved for all possible values of a given variable belonging usually to a convex set. We establish the convergence criteria of the Gauss-type proximal point algorithm, which guarantees the existence and the convergence of any sequence generated by this algorithm under mild conditions. More precisely, semilocal and local convergences of the Gauss-type proximal point algorithm are analyzed.
Variational inequality, Metrically regular mappings, Proximal point algorithm, Semi-local convergence
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