On the Convergence of Gauss-type Proximal Point Method for Smooth Generalized Equations
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 2, Issue 4
Abstract
Let X and Y be Banach spaces and Ω be an open subset of X. Let f : X → Y be a Fr´echet differentiable function on Ω and F : X 2Y be a set valued mapping with closed graph. We deal with smooth generalized equations which is defined by the sum of Fr´echet differentiable function and a set valued mapping. Under some sufficient conditions, a Gauss-type proximal point algorithm (G-PPA) is introduced and studied for solving generalized equations of the form 0 ∈ f(x) + F(x). Indeed, when F is metrically regular we analyze semi-local and local convergence of the G-PPA. Furthermore, we give a numerical example to justify the convergence results of the G-PPA.
Authors and Affiliations
Md. Asraful Alom, Mohammed Harunor Rashid
Keywords
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- EP ID EP338385
- DOI 10.9734/ARJOM/2017/31288
- Views 90
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