Related papers: Inexact reduced gradient methods in nonconvex opti…

We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified…

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…

We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…

In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…

In this paper, we introduce an inertial version of the Proximal Incremental Aggregated Gradient method (PIAG) for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function.…

We develop and analyze a variant of the SARAH algorithm, which does not require computation of the exact gradient. Thus this new method can be applied to general expectation minimization problems rather than only finite sum problems. While…

The proximal gradient method is a standard approach for solving composite minimization problems in which the objective function is the sum of a continuously differentiable function and a lower semicontinuous, extended-valued function. The…

Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…

In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz (PL) inequality. We establish that the PL inequality is a…

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…

This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of…

In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors' previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In…

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…

For deterministic optimization, line-search methods augment algorithms by providing stability and improved efficiency. We adapt a classical backtracking Armijo line-search to the stochastic optimization setting. While traditional…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex…

This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random…

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

Online and stochastic gradient methods have emerged as potent tools in large scale optimization with both smooth convex and nonsmooth convex problems from the classes $C^{1,1}(\reals^p)$ and $C^{1,0}(\reals^p)$ respectively. However to our…