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

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 p...

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Vydané v:TheScientificWorld Ročník 2013; číslo 2013; s. 1 - 6
Hlavní autori: Guo, Tiande, Zhao, Tong, Li, Mingqiang, Han, Congying
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013
John Wiley & Sons, Inc
Wiley
Predmet:
Algorithms
Applied mathematics
Artificial intelligence
Computational geometry
Constraints
Convex functions
Convexity
Decomposition
Hessian matrices
Inverse problems
Iterative methods
Linear functions
Mathematical analysis
Mathematical models
Mathematical research
Matrix methods
Methods
Optimization
Programming, Linear
Quadratic programming
Software
Support vector machines
ISSN:2356-6140, 1537-744X, 1537-744X
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Shrnutí: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. Itis proved that the new algorithm can terminate at an ε-optimal solution within O(1/ε) 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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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Academic Editors: I. Ahmad and P.-y. Nie
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2013/246596