Accelerated convergence rate – Optimization Online

UGM: A Unified Framework and New Perspectives for Accelerated Gradient Methods in Smooth and Strongly Convex Optimization

Published: 2026/08/31

Convex Optimization Accelerated Algorithms, Accelerated convergence rate

In this paper, we propose a unified framework for accelerated gradient methods, dubbed UGM, which subsumes a wide range of accelerated and conventional gradient-type methods designed for minimizing $L$-smooth and $\mu$-strongly convex functions. We demonstrate that the iteration update of the proposed framework can be intrinsically interpreted as a hybrid combination of the heavy-ball method … Read more

A faster proximal-indefinite augmented Lagrangian method with O(1/k^2 ) convergence rate

Published: 2025/05/05, Updated: 2025/12/29

Jianchao Bai

Convex and Nonsmooth Optimization Accelerated convergence rate, augmented lagrangian method, indefinite proximal term, Signal reconstruction

The Augmented Lagrangian Method (ALM), firstly proposed in 1969, remains a vital framework in large-scale constrained optimization. This paper addresses a linearly constrained composite convex minimization problem and presents a general proximal ALM that incorporates both Nesterov acceleration and relaxed acceleration, while enjoying a proximal-indefinite term. Under mild assumptions (potentially without requiring prior knowledge of … Read more