Variable Smoothing for Convex Optimization Problems Using Stochastic Gradients

Author:

Boţ Radu IoanORCID,Böhm Axel

Abstract

AbstractWe aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal–dual type methods are employed as they are effective and also well studied. However, under the additional assumption of Lipschitz continuity of the nonsmooth function which is composed with the linear operator we can derive novel algorithms through regularization via the Moreau envelope. Furthermore, we tackle large scale problems by means of stochastic oracle calls, very similar to stochastic gradient techniques. Applications to total variational denoising and deblurring, and matrix factorization are provided.

Funder

Austrian Science Fund

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis

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