The cubic spherical optimization problems (Q2894517)
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scientific article; zbMATH DE number 6051346
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The cubic spherical optimization problems |
scientific article; zbMATH DE number 6051346 |
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The cubic spherical optimization problems (English)
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29 June 2012
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cubic spherical optimization
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approximation solution
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polynomial time approximation scheme
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largest singular value
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numerical results
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0.92141294
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0.8978487
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0.8866106
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0.87816125
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0.87538576
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0.87061995
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0.8696954
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The authors first show that the cubic one-spherical and two-spherical optimization problems are special cases of the three-spherical optimization problem. This fact is used to improve the bounds of a theorem. Then they reformulate the cubic two-spherical optimization problem as an NP-hard quartic optimization problem over a unit sphere. As a result of this reformulation, NP-hardness of the cubic two-spherical and three-spherical optimization problems is established.NEWLINENEWLINEIn the rest of this paper, the authors focus on the cubic three-spherical optimization problem. They show that when some matrices are simultaneously diagonalized the problem is polynomial time solvable. Then they present a relative quality bound by finding the largest singular values of matrices. Finally, a practical method for solving the cubic three-spherical optimization problem is proposed and preliminary numerical results are reported.
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