The cubic spherical optimization problems

来源 :International Conference on the spectral theory of the tenso | 被引量 : 0次 | 上传用户：tshanyf

【摘要】

：

　　In this talk,the cubic spherical optimization problems,including the cubic one-spherical/two-spherical/three-spherical optimization problems,are discussed.W

【作者】

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Xinzhen Zhang

【机构】

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TianjinUniversity

【出处】

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International Conference on the spectral theory of the tenso

【发表日期】

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2012年5期

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　　In this talk,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 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.

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The cubic spherical optimization problems

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