Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25082
Title: Semidefinite relaxation approximation for multivariate bi-quadratic optimization with quadratic constraints
Authors: Ling, C
Zhang, X
Qi, L 
Keywords: Approximation solution
Bi-quadratic optimization
NP-hard
Semidefinite programming relaxation
Issue Date: 2012
Publisher: John Wiley & Sons
Source: Numerical linear algebra with applications, 2012, v. 19, no. 1, p. 113-131 How to cite?
Journal: Numerical linear algebra with applications 
Abstract: In this paper, we consider the NP-hard problem of finding global minimum of quadratically constrained multivariate bi-quadratic optimization. We present some bounds of the considered problem via approximately solving the related bi-linear semidefinite programming (SDP) relaxation. Based on the bi-linear SDP relaxation, we also establish some approximation solution methods, which generalize the methods for the quadratic polynomial optimization in (SIAM J. Optim. 2003; 14:268-283). Finally, we present a special form, whose bi-linear SDP relaxation can be approximately solved in polynomial time.
URI: http://hdl.handle.net/10397/25082
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.781
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