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An optimal subgradient algorithm for large-scale bound-constrained convex optimization. (English) Zbl 1380.90215
Summary: 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.

##### MSC:
 90C25 Convex programming 90C60 Abstract computational complexity for mathematical programming problems 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods 68Q25 Analysis of algorithms and problem complexity
##### Software:
LBFGS-B; NNLS; OSGA; TRON
Full Text:
##### References:
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