On solving biquadratic optimization via semidefinite relaxation
In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several different constraints, we present variational approaches for solving them and give provable estimation for the approximation solutions. Some numerical results are reported at the end of this paper. Copyright Springer Science+Business Media, LLC 2012
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Volume (Year): 53 (2012)
Issue (Month): 3 (December)
Pages: 845-867
| Handle: | RePEc:spr:coopap:v:53:y:2012:i:3:p:845-867 |
| Contact details of provider: | Web page: http://www.springer.com
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| Order Information: | Web: http://www.springer.com/math/journal/10589 |
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- NESTEROV, Yurii, 1997. "Semidefinite relaxation and nonconvex quadratic optimization," CORE Discussion Papers 1997044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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