Related papers: Boosting First-Order Methods by Shifting Objective…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
We study convex-concave saddle point problems with bilinear coupling, covering linearly constrained convex optimization and more general nonsmooth or constrained models via a proximable term in the dual objective. In linearly convergent…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…
First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…
First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with…
We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning…
We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…
Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…
We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…