Hello, Thanks for reply! But I think that solution is right without the constrain b'b=1. With this constrain, the solution is not so simple. :( Regards, Yingfu
________________________________ Från: Rolf Turner [mailto:[EMAIL PROTECTED] Skickat: on 2006-08-09 18:08 Till: Yingfu Xie; [email protected] Ämne: Re: [R] minimization a quadratic form with some coef fixed and some constrained Yingfu Xie wrote: > I had problems with an extension to a classic optimization problem. > > The target is to minimize a quadratic form a'Ma with respect to vector > b, where vector a=(b',-1)', i.e., a is the expand of b, and M is a > symmetric matrix (positive definite if needed). One more constrain on b > is b'b=1. I want to solve b given M. > > I tried but it seems impossible to find an analytic solution for b. Any > objection? > > Now, come to the numerical. Does anybody have any idea on how to > parameterize this to use, e.g. optim() or constrOptim()? > > Any help are appreciated very much! The analytic solution is trivial. Write M as | M_11 c | | c' m | Then given that M_11 is positive definite, the minimizer is b = (M_11)^{-1}c cheers, Rolf Turner [EMAIL PROTECTED] ########################################### This message has been scanned by F-Secure Anti-Virus for Mic...{{dropped}}
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