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Computing Proximal Points of Convex Functions with Inexact Subgradients.
- Source :
- Set-Valued & Variational Analysis; Sep2018, Vol. 26 Issue 3, p469-492, 24p
- Publication Year :
- 2018
-
Abstract
- Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact function values are at hand, but exact subgradients are either not available or not useful. We use approximate subgradients to build a model of the objective function, and prove that the method converges to the true prox-point within acceptable tolerance. The subgradient g<subscript>k</subscript> used at each step k is such that the distance from g<subscript>k</subscript> to the true subdifferential of the objective function at the current iteration point is bounded by some fixed ε > 0. The algorithm includes a novel tilt-correct step applied to the approximate subgradient. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 18770533
- Volume :
- 26
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Set-Valued & Variational Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 131207304
- Full Text :
- https://doi.org/10.1007/s11228-016-0394-3