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Recently, deep matrix factorization has been established as a powerful model for unsupervised tasks, achieving promising results, especially for multi-view clustering. However, existing methods often lack effective feature selection…

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…

Cyclic block coordinate methods are a fundamental class of first-order algorithms, widely used in practice for their simplicity and strong empirical performance. Yet, their theoretical behavior remains challenging to explain, and setting…

This work considers the decentralized successive convex approximation (SCA) method for minimizing stochastic non-convex objectives subject to convex constraints, along with possibly non-smooth convex regularizers. Although SCA has been…

We show how one can obtain nonaccelerated randomized coordinate descent method (Yu. Nesterov, 2010) and nonaccelerated method of randomization of sum-type functional (Le Roux-Schmidt-Bach, 2012) from the optimal method for the stochastic…

In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…

Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…

Non-concave maximization has been the subject of much recent study in the optimization and machine learning communities, specifically in deep learning. Recent papers Ge et al, Lee et al (and references therein) indicate that first order…

Multi-source learning is an emerging area of research in statistics, where information from multiple datasets with heterogeneous distributions is combined to estimate the parameter of interest for a target population without observed…

The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility…

In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems. We prove the…

We study decentralized asynchronous multiagent optimization over networks, modeled as static (possibly directed) graphs. The optimization problem consists of minimizing a (possibly nonconvex) smooth function--the sum of the agents' local…

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

This paper is devoted to some approaches for convex min-min problems with smoothness and strong convexity in only one of the two variable groups. It is shown that the proposed approaches, based on Vaidya's cutting plane method and…

We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide class of applications, such as the augmented Lagrangian…

Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…

In this paper, a distributed convex optimization algorithm, termed \emph{distributed coordinate dual averaging} (DCDA) algorithm, is proposed. The DCDA algorithm addresses the scenario of a large distributed optimization problem with…

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…