相关论文: Lipschitz gradients for global optimization in a o…

The work is devoted to the construction of efficient and applicable to real tasks first-order methods of convex optimization, that is, using only values of the target function and its derivatives. Construction uses OGM-G, fast gradient…

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…

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 consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…

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…

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…

Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…

A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…

Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…

In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the…

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…

The paper presents a new descent algorithm for locally Lipschitz continuous functions $f:X\to\mathbb{R}$. The selection of a descent direction at some iteration point $x$ combines an approximation of the set-valued gradient of $f$ on a…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…