Related papers: A globally convergent difference-of-convex algorit…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
Imaging tasks are typically tackled using a structured optimization framework. This paper delves into a class of algorithms for difference-of-convex (DC) structured optimization, focusing on minimizing a DC function along with a possibly…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
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…
Minimax optimization plays an important role in many machine learning tasks such as generative adversarial networks (GANs) and adversarial training. Although recently a wide variety of optimization methods have been proposed to solve the…
Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for {convex} consensus optimization. However, to the behaviors or consensus \emph{nonconvex} optimization,…
We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…
We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…
Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…
This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms…
This paper presents a decentralized algorithm for solving distributed convex optimization problems in dynamic networks with time-varying objectives. The unique feature of the algorithm lies in its ability to accommodate a wide range of…
In this paper we consider the difference-of-convex (DC) programming problems, whose objective function is the difference of two convex functions. The classical DC Algorithm (DCA) is well-known for solving this kind of problems, which…
This paper concerns a class of constrained difference-of-convex (DC) optimization problems in which, the constraint functions are continuously differentiable and their gradients are strictly continuous. For such nonconvex and nonsmooth…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…
We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the $\ell_1$ penalty function for solving nonsmooth DC optimization problems with nonsmooth DC equality and inequality constraints. The method…
We consider the difference of convex (DC) optimization problem subject to box constraints. Utilizing epsilon-subdifferentials of DC components of the objective, we develop a new method for finding global solutions to this problem. The…