Related papers: Accelerated Bregman gradient methods for relativel…

Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significantly expanded the class of problems for which optimal…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

In this paper we study the problems of minimizing the sum of two nonconvex functions: one is differentiable and satisfies smooth adaptable property. The smooth adaptable property, also named relatively smooth condition, is weaker than the…

Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails in many important problem classes like quadratic inverse…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

We consider the problem of minimizing the sum of a Lipschitz differentiable convex function $f$ and a proper closed convex function $h$ that admits efficient linear minimization oracles, subject to multiple smooth convex inequality…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is "simple". We provide a Bregman-type algorithm…

In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…

Due to its applications in many different places in machine learning and other connected engineering applications, the problem of minimization of a smooth function that satisfies the Polyak-{\L}ojasiewicz condition receives much attention…

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

We show that standard extragradient methods (i.e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide a fine-grained…

Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…

We show that the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems can be viewed as an inexact gradient method applied to the primal problem. The gradient, whose exact…

We introduce a unified algorithmic framework, called proximal-like incremental aggregated gradient (PLIAG) method, for minimizing the sum of a convex function that consists of additive relatively smooth convex components and a proper lower…

It is well-known that accelerated gradient first order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However,…