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Convergence analysis of a block improvement method for polynomial optimization over unit spheres. (English) Zbl 1374.65105
Summary: We study the convergence property of a block improvement method (BIM) for the bi-quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second-order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising.

MSC:
65K05 Numerical mathematical programming methods
90C22 Semidefinite programming
90C20 Quadratic programming
Software:
minpack; Matlab
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