Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30199
Title: The cubic spherical optimization problems
Authors: Zhang, X
Qi, L 
Ye, Y 
Keywords: Approximation solution
Cubic spherical optimization
Polynomial time approximation scheme (PTAS)
Issue Date: 2012
Source: Mathematics of computation, 2012, v. 81, no. 279, p. 1513-1525 How to cite?
Journal: Mathematics of Computation 
Abstract: In this paper, the cubic spherical optimization problems, including the cubic one-spherical/two-spherical/three-spherical optimization problems, are discussed. We first show that the two-spherical optimization problem is a special case of the three-spherical optimization problem. Then we show that the one-spherical optimization problem and the two-spherical optimization problem have the same optimal value when the tensor is symmetric. In addition, NP-hardness of them are established. For the cubic three-spherical optimization problem, we discuss the conditions under which the problem is polynomial time solvable and if the polynomial time approximation scheme (PTAS) exists. Then we 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.
URI: http://hdl.handle.net/10397/30199
ISSN: 0025-5718
DOI: 10.1090/S0025-5718-2012-02577-4
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