Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 469–492 | Cite as

Computing Proximal Points of Convex Functions with Inexact Subgradients

  • W. Hare
  • C. Planiden


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 k used at each step k is such that the distance from g k 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.


Bundle methods Convex optimization Cutting-plane methods Inexact subgradient Proximal point 

Mathematics Subject Classifications

Primary 49M30 65K10 Secondary 90C20 90C56 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.MathematicsUniversity of British ColumbiaKelownaCanada

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