# Optimization of Inf-Convolution Regularized Nonconvex Composite Problems

arXiv: https://arxiv.org/abs/1903.11690 · HTML: https://mlsanity.com/paper/1903.11690/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives](https://mlsanity.com/paper/2605.11850/) (2026)

## Abstract (arXiv)

In this work, we consider nonconvex composite problems that involve inf-convolution with a Legendre function, which gives rise to an anisotropic generalization of the proximal mapping and Moreau-envelope. In a convex setting such problems can be solved via alternating minimization of a splitting formulation, where the consensus constraint is penalized with a Legendre function. In contrast, for nonconvex models it is in general unclear that this approach yields stationary points to the infimal convolution problem. To this end we analytically investigate local regularity properties of the Moreau-envelope function under prox-regularity, which allows us to establish the equivalence between stationary points of the splitting model and the original inf-convolution model. We apply our theory to characterize stationary points of the penalty objective, which is minimized by the elastic averaging SGD (EASGD) method for distributed training. Numerically, we demonstrate the practical relevance of the proposed approach on the important task of distributed training of deep neural networks.