Related papers: Optimal convergence rates for Nesterov acceleratio…

The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. However, for smooth objectives, its best-known convergence rate remains suboptimal, and whether PBM can be accelerated…

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 consider distributed optimization in random networks where N nodes cooperatively minimize the sum \sum_{i=1}^N f_i(x) of their individual convex costs. Existing literature proposes distributed gradient-like methods that are…

Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient…

We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…

We investigate the integration of Nesterov-type acceleration into primal-dual methods for structured convex optimization. While proximal splitting algorithms efficiently handle composite problems of the form $\min_x f(x)+g(x)+h(Kx)$,…

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are…

In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and…

We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…

We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…

Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…

Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…

We study convergence rates of the classic proximal bundle method for a variety of nonsmooth convex optimization problems. We show that, without any modification, this algorithm adapts to converge faster in the presence of smoothness or a…

In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…

We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization…

We prove convergence rates of Stochastic Zeroth-order Gradient Descent (SZGD) algorithms for Lojasiewicz functions. The SZGD algorithm iterates as \begin{align*} \mathbf{x}_{t+1} = \mathbf{x}_t - \eta_t \widehat{\nabla} f (\mathbf{x}_t),…

We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring…