标题： 无相对光滑性的凸最小化无线搜索自适应Bregman邻近梯度 显示英文标题

标题： Linesearch-free adaptive Bregman proximal gradient for convex minimization without relative smoothness

摘要： 本文介绍了自适应Bregman邻近梯度算法，用于解决凸复合最小化问题，而无需依赖全局相对光滑性或强凸性假设。 在最近自适应步长选择进展的基础上，所提出的方法基于局部曲率估计生成步长，完全消除了对回溯线搜索的需求。 一个关键创新是Young不等式的Bregman推广，这允许根据更新中使用的相同Bregman距离来控制一个关键的内积。 我们的理论适用于可微项仅相对于一个生成距离函数局部光滑的问题，而无需全局模量或对称系数的存在。 数值实验表明，它们在各种问题类别中与现有方法相比表现出竞争力。 显示英文摘要

摘要： 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 stepsize selections, the proposed methods generate stepsizes based on local curvature estimates, entirely eliminating the need for backtracking linesearch. A key innovation is a Bregman generalization of Young's inequality, which allows controlling a critical inner product in terms of the same Bregman distances used in the updates. Our theory applies to problems where the differentiable term is merely locally smooth relative to a distance-generating function, without requiring the existence of global moduli or symmetry coefficients. Numerical experiments demonstrate their competitive performance compared to existing approaches across various problem classes.