Year: 2016
Type: article
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 (an 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.
Source: SIAM Journal on Optimization
DOI: 10.1137/15m1027371
Author: James Renegar
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2406180247