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arXiv · 1404.4805

iPiano: Inertial Proximal Algorithm for Non-Convex Optimization

Peter Ochs·Yunjin Chen·Thomas Brox·Thomas Pock
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Abstract

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a non-smooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on non-convex problems. The convergence result is obtained based on the \KL inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and, then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems: image denoising with learned priors and diffusion based image compression.

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Peter Ochs, Yunjin Chen, Thomas Brox, Thomas Pock. 2014-04-18. iPiano: Inertial Proximal Algorithm for Non-Convex Optimization. https://arxiv.org/abs/1404.4805

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