Convergence Analysis of Generalized Non-Smooth Equations Using Gauss-Type Proximal Point Method

This work discusses the Gauss-type proximal point algorithm for solving non-smooth generalized equations like 0 ∈ q(x) + Q(x), where a set-valued mapping Q : X ⇉ 2Y acting between two real or complex Banach spaces X and Y with closed graph and q: U ⊆ X→Y is a single-valued mapping. In order to ensure the existence as well as convergence of any sequence produced by this algorithm under appropriate circumstances, we develop the convergence criteria of this approach by utilize metric regularity condition and point-based approximation. Lastly, we present a numerical example to validate the semi-local convergence of this algorithm.