Related papers: A nonsmooth nonconvex descent algorithm
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…
We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\epsilon^{-7/4} \log(1/ \epsilon) )$ to find an $\epsilon$-stationary point,…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
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…
We consider the optimization problem of the form $\min_{x \in \mathbb{R}^d} f(x) \triangleq \mathbb{E}_{\xi} [F(x; \xi)]$, where the component $F(x;\xi)$ is $L$-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro factorization, but these approaches can suffer from slow convergence, especially when dealing with solutions characterized by a large condition number,…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense. Specifically, motivated by a recent flurry of activity on…
We propose a bundle trust-region algorithm to minimize locally Lipschitz functions which are potentially nonsmooth and nonconvex. We prove global convergence of our method and show by way of an example that the classical convergence…
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…
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…