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摘要:
It is known that computing the largest (smallest) Z-eigenvalue of a symmetric tensor is equivalent to maximizing (minimizing) a homogenous polynomial over the unit sphere. Based on such a reformulation, we shall propose a feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors. One basic feature of the method is that the true Hessian, which is ready for polynomials, is utilized in the trust-region subproblem so that any cluster point of the iterations can be shown to satisfy the second-order necessary conditions. The other feature is that after a trial step d(k) is provided by solving the trust-region subproblem at the current point x(k), the projection of x(k) + d(k) to the unit sphere, instead of the point x(k) + d(k) itself, is judged and if successful, is used for the next point. Global convergence and local quadratic convergence of the feasible trust-region method are established for the tensor Z-eigenvalue problem. The preliminary numerical results over several testing problems show that the feasible trust-region method is quite promising.
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来源 :
PACIFIC JOURNAL OF OPTIMIZATION
ISSN: 1348-9151
年份: 2015
期: 2
卷: 11
页码: 291-307
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JCR@2022
ESI学科: ENGINEERING;
ESI高被引阀值:174
JCR分区:4
中科院分区:4
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