相关论文: Locally Accelerated Conditional Gradients

We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…

Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard…

In this paper, we deal with multiobjective composite optimization problems, where each objective function is a combination of smooth and possibly non-smooth functions. We first propose a parameter-dependent conditional gradient method to…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

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…

In this paper we develop accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient (LLCG), which is beyond the well-studied class of convex optimization with Lipschitz continuous gradient. In…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…

We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…

This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a…

Analyses of accelerated (momentum-based) gradient descent usually assume bounded condition number to obtain exponential convergence rates. However, in many real problems, e.g., kernel methods or deep neural networks, the condition number,…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…

Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of…

Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…