"Efficient" Subgradient Methods for General Convex Optimization
Abstract
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified error of optimality. Feasibility is maintained with a line-search at each iteration, avoiding the need for orthogonal projections onto the feasible region (the operation that limits practicality of traditional subgradient methods). Lipschitz continuity is not required, yet the algorithm is shown to possess a convergence rate analogous to rates for traditional methods, albeit with error measured relatively, whereas traditionally error has been absolute. The algorithm is derived using an elementary framework that can be utilized to design other such algorithms.
Cite
@article{arxiv.1605.08712,
title = {"Efficient" Subgradient Methods for General Convex Optimization},
author = {James Renegar},
journal= {arXiv preprint arXiv:1605.08712},
year = {2016}
}
Comments
This article supersedes our arXiv posting arXiv:1503.02611, in fully developing results for general convex optimization. The extensions were made in response to suggestions from reviewers for positioning the work so as to attract a broad audience