On the coupled continuous knapsack problems: projection onto the volume constrained Gibbs N-simplex

Coupled continuous quadratic knapsack problems (CCK) are introduced in the present study. The solution of a CCK problem is equivalent to the projection of an arbitrary point onto the volume constrained Gibbs N-simplex, which has a wide range of applications in computational science and engineering....

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Bibliographic Details
Published in:Optimization letters Vol. 10; no. 1; pp. 137 - 158
Main Author: Tavakoli, Rouhollah
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Linearly constrained optimization
90C20
65K05
91B32
Convex optimization
90C25
Time-linear algorithm
Knapsack problem
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:Coupled continuous quadratic knapsack problems (CCK) are introduced in the present study. The solution of a CCK problem is equivalent to the projection of an arbitrary point onto the volume constrained Gibbs N-simplex, which has a wide range of applications in computational science and engineering. Three algorithms have been developed in the present study to solve large scale CCK problems. According to the numerical experiments of this study, the computational costs of presented algorithms scale linearly with the problem size, when it is sufficiently large. Moreover, they show competitive or even superior computational performance compared to the advanced QP solvers. The ease of implementation and linear scaling of memory usage with the problem size are the other benefits of the presented algorithms.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-015-0866-7