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

Masoud Ahookhosh () and Arnold Neumaier ()
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Masoud Ahookhosh: University of Vienna
Arnold Neumaier: University of Vienna

Mathematical Methods of Operations Research, 2017, vol. 86, issue 1, No 5, 123-147

Abstract: 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.

Keywords: Bound-constrained convex optimization; Nonsmooth optimization; First-order black-box oracle; Subgradient methods; Optimal complexity; High-dimensional data; 90C25; 90C60; 49M37; 65K05; 68Q25 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00186-017-0585-1

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