proximal splitting algorithms – Optimization Online

Swapping objectives accelerates Davis-Yin splitting

Published: 2025/06/30

Convex Optimization, Nonsmooth Optimization complexity, convex optimization, Davis-Yin splitting, douglas-rachford splitting, first-order methods, proximal splitting algorithms

In this work, we investigate the application of Davis–Yin splitting (DYS) to convex optimization problems and demonstrate that swapping the roles of the two nonsmooth convex functions can result in a faster convergence rate. Such a swap typically yields a different sequence of iterates, but its impact on convergence behavior has been largely understudied or … Read more

The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates

Published: 2018/01/06

Radu Ioan Bot

Dang-Khoa Nguyen

Nonsmooth Optimization alternating direction method of multipliers, convergence analysis, convergence rate, kurdyka-lojasiewicz inequality, lojasiewicz exponent, nonconvex complexly structured optimization problems, proximal splitting algorithms, variable metric

We propose two numerical algorithms for minimizing the sum of a smooth function and the composition of a nonsmooth function with a linear operator in the fully nonconvex setting. The iterative schemes are formulated in the spirit of the proximal and, respectively, proximal linearized alternating direction method of multipliers. The proximal terms are introduced through … Read more