A Framework for Analyzing Local Convergence Properties with Applications to Proximal-Point Algorithms

Y. D. Dong and A. Fischer
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Y. D. Dong: Zhengzhou University
A. Fischer: Technische Universität Dresden

Journal of Optimization Theory and Applications, 2006, vol. 131, issue 1, No 4, 53-68

Abstract: Abstract A general algorithmic scheme for solving inclusions in a Banach space is investigated in respect to its local convergence behavior. Particular emphasis is placed on applications to certain proximal-point-type algorithms in Hilbert spaces. The assumptions do not necessarily require that a solution be isolated. In this way, results existing for the case of a locally unique solution can be extended to cases with nonisolated solutions. Besides the convergence rates for the distance of the iterates to the solution set, strong convergence to a sole solution is shown as well. As one particular application of the framework, an improved convergence rate for an important case of the inexact proximal-point algorithm is derived.

Keywords: Inclusions; generalized equations; local convergence; upper Lipschitz continuity; nonisolated solutions; proximal-point algorithms (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9126-4

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