相关论文: A Bregman forward-backward linesearch algorithm fo…

This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient…

We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of…

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…

Optimizing strongly convex functions subject to linear constraints is a fundamental problem with numerous applications. In this work, we propose a block (accelerated) randomized Bregman-Kaczmarz method that only uses a block of constraints…

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…

When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may…

This paper is devoted to minimizing the sum of a smooth function and a nonsmooth $\ell_1$-regularized term. This problem as a special cases includes the $\ell_1$-regularized convex minimization problem in signal processing, compressive…

We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave…

In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…

In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, for the problem of minimizing a class of convex objective…

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized DC (Difference-of-Convex functions) programming, which is minimizing the sum of two separable DC parts and one…