Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method

Abstract

Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈ h ( x ) + H ( x ), where h : X → Y is a smooth function on Ω ⊆ X and H : X ⇉ 2 Y is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.