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The task of approximating an arbitrary convex function arises in several learning problems such as convex regression, learning with a difference of convex (DC) functions, and learning Bregman or $f$-divergences. In this paper, we develop…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
In prior works, stochastic dual coordinate ascent (SDCA) has been parallelized in a multi-core environment where the cores communicate through shared memory, or in a multi-processor distributed memory environment where the processors…
This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…
Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range of machine learning models. However, the current theoretical understanding of its convergence rate is far from…
We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…
Inspired by the Optimistic Gradient Ascent-Proximal Point Algorithm (OGAProx) proposed by Bo{\c{t}}, Csetnek, and Sedlmayer for solving a saddle-point problem associated with a convex-concave function with a nonsmooth coupling function and…
The image restoration problem is one of the popular topics in image processing studied by many authors on account of its applications in various areas. The aim of this paper is to present a new algorithm by using viscosity approximation…
We present a forward-backward-based algorithm to minimize a sum of a differentiable function and a nonsmooth function, both being possibly nonconvex. The main contribution of this work is to consider the challenging case where the nonsmooth…
A general method for recovering missing DCT coefficients in DCT-transformed images is presented in this work. We model the DCT coefficients recovery problem as an optimization problem and recover all missing DCT coefficients via linear…
In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
This paper is devoted to a detailed convergence analysis of the method of codifferential descent (MCD) developed by professor V.F. Demyanov for solving a large class of nonsmooth nonconvex optimization problems. We propose a generalization…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Nonconvex constrained optimization problems can be used to model a number of machine learning problems, such as multi-class Neyman-Pearson classification and constrained Markov decision processes. However, such kinds of problems are…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…