An optimal subgradient algorithm for large-scale bound-constrained convex optimization

An optimal subgradient algorithm for large-scale bound-constrained convex optimization This paper shows that the optimal subgradient algorithm (OSGA)—which uses first-order information to solve convex optimization problems with optimal complexity—can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This is done by constructing an explicit method as well as an inexact scheme for solving the bound-constrained rational subproblem required by OSGA. This leads to an efficient implementation of OSGA on large-scale problems in applications arising from signal and image processing, machine learning and statistics. Numerical experiments demonstrate the promising performance of OSGA on such problems. A software package implementing OSGA for bound-constrained convex problems is available. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods of Operations Research Springer Journals

An optimal subgradient algorithm for large-scale bound-constrained convex optimization

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Publisher
Springer Journals
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Operations Research/Decision Theory; Business and Management, general
ISSN
1432-2994
eISSN
1432-5217
D.O.I.
10.1007/s00186-017-0585-1
Publisher site
See Article on Publisher Site

Abstract

This paper shows that the optimal subgradient algorithm (OSGA)—which uses first-order information to solve convex optimization problems with optimal complexity—can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This is done by constructing an explicit method as well as an inexact scheme for solving the bound-constrained rational subproblem required by OSGA. This leads to an efficient implementation of OSGA on large-scale problems in applications arising from signal and image processing, machine learning and statistics. Numerical experiments demonstrate the promising performance of OSGA on such problems. A software package implementing OSGA for bound-constrained convex problems is available.

Journal

Mathematical Methods of Operations ResearchSpringer Journals

Published: Apr 12, 2017

References

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