Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities |
| |
Authors: | Alfred Auslender Marc Teboulle |
| |
Affiliation: | (1) Institut Camille Jordan, University of Lyon I, Lyon, France;(2) School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978, Israel |
| |
Abstract: | We study subgradient projection type methods for solving non-differentiable convex minimization problems and monotone variational inequalities. The methods can be viewed as a natural extension of subgradient projection type algorithms, and are based on using non-Euclidean projection-like maps, which generate interior trajectories. The resulting algorithms are easy to implement and rely on a single projection per iteration. We prove several convergence results and establish rate of convergence estimates under various and mild assumptions on the problem’s data and the corresponding step-sizes. We dedicate this paper to Boris Polyak on the occasion of his 70th birthday. |
| |
Keywords: | Non-differentiable convex optimization Variational inequalities Ergodic convergence Subgradient methods Interior projection-like maps |
本文献已被 SpringerLink 等数据库收录! |