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ASYMPTOTIC CONVERGENCE ANALYSIS OF A NEW CLASS OF PROXIMAL POINT METHODS.
- Source :
-
SIAM Journal on Control & Optimization . 2007, Vol. 46 Issue 5, p1683-1704. 22p. - Publication Year :
- 2007
-
Abstract
- Finite dimensional local convergence results for self-adaptive proximal point methods and nonlinear functions with multiple minimizers are generalized and extended to a Hilbert space setting. The principle assumption is a local error bound condition which relates the growth in the function to the distance to the set of minimizers. A local convergence result is established for almost exact iterates. Less restrictive acceptance criteria for the proximal iterates are also analyzed. These criteria are expressed in terms of a subdifferential of the proximal function and either a subdifferential of the original function or an iteration difference. If the proximal regularization parameter μ(x) is sufficiently small and bounded away from zero and f is sufficiently smooth, then there is local linear convergence to the set of minimizers. For a locally convex function, a convergence result similar to that for almost exact iterates is established. For a locally convex solution set and smooth functions, it is shown that if the proximal regularization parameter has the form μ(x) = β∥f′[x]∥η, where η ϵ (0, 2), then the convergence is at least superlinear if η ϵ (0, 1) and at least quadratic if η [1, 2). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03630129
- Volume :
- 46
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Control & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 27745680
- Full Text :
- https://doi.org/10.1137/060666627