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The Scientific World Journal
Volume 2013, Article ID 246596, 6 pages
Research Article

An Accelerated Proximal Gradient Algorithm for Singly Linearly Constrained Quadratic Programs with Box Constraints

1School of Mathematical Sciences, University of Chinese Academy of Sciences, Shijingshan District, Beijing 100049, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China

Received 4 August 2013; Accepted 23 September 2013

Academic Editors: I. Ahmad and P.-y. Nie

Copyright © 2013 Congying Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recently, the existed proximal gradient algorithms had been used to solve non-smooth convex optimization problems. As a special nonsmooth convex problem, the singly linearly constrained quadratic programs with box constraints appear in a wide range of applications. Hence, we propose an accelerated proximal gradient algorithm for singly linearly constrained quadratic programs with box constraints. At each iteration, the subproblem whose Hessian matrix is diagonal and positive definite is an easy model which can be solved efficiently via searching a root of a piecewise linear function. It is proved that the new algorithm can terminate at an -optimal solution within iterations. Moreover, no line search is needed in this algorithm, and the global convergence can be proved under mild conditions. Numerical results are reported for solving quadratic programs arising from the training of support vector machines, which show that the new algorithm is efficient.