The problem of finding a zero point of a maximal monotone operator plays a central role in
modeling many application problems arising from various fields, and the proximal point …

We survey optimization problems that involve the cardinality of variable vectors in
constraints or the objective function. We provide a unified viewpoint on the general problem …

We consider the training of structured neural networks where the regularizer can be non-
smooth and possibly non-convex. While popular machine learning libraries have resorted to …

This paper proposes a method for designing diagonal preconditioners for a preconditioned
primal-dual splitting method (P-PDS), an efficient algorithm that solves nonsmooth convex …

Optimization problems with composite functions consist of an objective function which is the
sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the …

Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing
regression problems in machine learning. State of the art approaches are more efficient but …

Non-smooth optimization is a core ingredient of many imaging or machine learning
pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity …

We consider a variable metric and inexact version of the fast iterative soft-thresholding
algorithm (FISTA) type algorithm considered in [L. Calatroni and A. Chambolle, SIAM J …

This paper deals with a general framework for inexact forward--backward algorithms aimed
at minimizing the sum of an analytic function and a lower semicontinuous, subanalytic …

The primal-dual hybrid gradient (PDHG) algorithm is popular in solving min-max problems
which are being widely used in a variety of areas. To improve the applicability and efficiency …