Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method
Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method作者机构：Department of Mathematics Khulna University of Engineering & Technology Khulna Bangladesh
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2022年第13卷第6期
页 面：523-537页
学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学]
主 题：Set-Valued Mapping Metrically Regular Mapping Smooth Function Lipschitz-Like Mapping Semi-Local Convergence
摘 要：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 ⇉2Y 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.
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