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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Vydáno v:Optimization letters Ročník 10; číslo 1; s. 137 - 158
Hlavní autor: Tavakoli, Rouhollah
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016
Témata:
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
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Popis
Shrnutí: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