Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function

Jean-Philippe Chancelier

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arXiv · 1508.02994

Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function

Jean-Philippe Chancelier

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Abstract

In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principleor inexact variable metric forward-backward algorithm. Assuming that the global objective function satisfies the Kurdyka-Lojasiewicz inequalitywe prove the convergence of the proposed algorithm weakening assumptions found in previous works.

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BibTeX RIS

Jean-Philippe Chancelier. 2016-09-10. Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function. https://arxiv.org/abs/1508.02994

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