NDLI: New results on Hermitian matrix rank-one decomposition

Content Provider	Springer Nature Link
Author	Huang, Yongwei Ai, Wenbao Zhang, Shuzhong
Copyright Year	2009
Abstract	In this paper, we present several new rank-one decomposition theorems for Hermitian positive semidefinite matrices, which generalize our previous results in Huang and Zhang (Math Oper Res 32(3):758–768, 2007), Ai and Zhang (SIAM J Optim 19(4):1735–1756, 2009). The new matrix rank-one decomposition theorems appear to have wide applications in theory as well as in practice. On the theoretical side, for example, we show how to further extend some of the classical results including a lemma due to Yuan (Math Program 47:53–63, 1990), the classical results on the convexity of the joint numerical ranges (Pang and Zhang in Unpublished Manuscript, 2004; Au-Yeung and Poon in Southeast Asian Bull Math 3:85–92, 1979), and the so-called Finsler’s lemma (Bohnenblust in Unpublished Manuscript; Au-Yeung and Poon in Southeast Asian Bull Math 3:85–92, 1979). On the practical side, we show that the new results can be applied to solve two typical problems in signal processing and communication: one for radar code optimization and the other for robust beamforming. The new matrix decomposition theorems are proven by construction in this paper, and we demonstrate that the constructive procedures can be implemented efficiently, stably, and accurately. The URL of our Matlab programs is given in this paper. We strongly believe that the new decomposition procedures, as a means to solve non-convex quadratic optimization with a few quadratic constraints, are useful for many other potential engineering applications.
Ending Page	283
Page Count	31
Starting Page	253
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	128
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-08-21
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Joint numerical range Theoretical, Mathematical and Computational Physics Linear programming Matrix rank-one decomposition Interior-point methods Positive semidefinite Hermitian matrix Complementarity and equilibrium problems and variational inequalities (finite dimensions) Mathematical Methods in Physics Quadratic optimization Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Numerical Analysis Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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