相关论文: Global Convergence of Arbitrary-Block Gradient Met…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principleor inexact variable…
Proximal gradient methods are a popular tool for the solution of structured, nonsmooth minimization problems. In this work, we investigate an extension of the former to general Banach spaces and provide worst-case convergence rates for,…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: $L(x,y)=f(x)+Q(x,y)+g(y)$, where $f:\R^n\rightarrow\R\cup{+\infty}$ and $g:\R^m\rightarrow\R\cup{+\infty}$…
The difference-of-convex algorithm (DCA) is a conceptually simple method for the minimization of (possibly) nonconvex functions that are expressed as the difference of two convex functions. At each iteration, DCA constructs a global…
Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…
In this paper we present an abstract convergence analysis of inexact descent methods in Riemannian context for functions satisfying Kurdyka-Lojasiewicz inequality. In particular, without any restrictive assumption about the sign of the…
The conditions of relative smoothness and relative strong convexity were recently introduced for the analysis of Bregman gradient methods for convex optimization. We introduce a generalized left-preconditioning method for gradient descent,…
In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…
This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…
In this work, we propose an adaptive variation on the classical Heavy-ball method for convex quadratic minimization. The adaptivity crucially relies on so-called "Polyak step-sizes", which consists in using the knowledge of the optimal…
In this paper we analyze a family of general random block coordinate descent methods for the minimization of $\ell_0$ regularized optimization problems, i.e. the objective function is composed of a smooth convex function and the $\ell_0$…
The Polyak-{\L}ojasiewicz (P{\L}) condition is often invoked in nonconvex optimization because it allows fast convergence of algorithms beyond strong convexity. A function $f \colon \mathcal{M} \to \mathbb{R}$ on a Riemannian manifold…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…