[R] Maximization of quadratic forms

Ravi Varadhan rvaradhan at jhmi.edu
Wed May 19 04:52:06 CEST 2010

Hi Taki,

This should be doable with "gnls" by properly specifying the `weights' argument, although I cannot figure out how to do it without spending much time (someone like Doug Bates would know for sure).

But let me ask you:  did you try the straightforward nonlinear optimization (e.g. optim)?  Did you run into any convergence problems?  Did it take way too much time?   

If \mu(\beta) is not a nasty function, you should be able to provide analytic gradient for your objective function.  This would make nonlinear optimization quite efficient.  



Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu

----- Original Message -----
From: Russell Shinohara <rshinoha at jhsph.edu>
Date: Tuesday, May 18, 2010 2:38 pm
Subject: [R] Maximization of quadratic forms
To: r-help at r-project.org

> Dear R Help,
>  I am trying to fit a nonlinear model for a mean function 
> $\mu(Data_i,\beta)$ for a fixed covariance matrix where $\beta$ and 
> $\mu$ are low-dimensional. More specifically, for fixed 
> variance-covariance matrices $\Sigma_{z=0}$ and $\Sigma_{z=1}$ 
> (according to a binary covariate $Z$), I am trying to minimize:
>  $\sum_{i=1^n} (Y_i-\mu_(Data_i,\beta))' \Sigma_{z=z_i}^{-1} (Y_i-\mu_(Data_i,\beta))$
>  in terms of the parameter $\beta$. Is there a way to do this in R in 
> a more stable and efficient fashion than just using a general 
> optimization function such as optim? I have tried to use gnls, but I 
> was unsuccessful in specifying different values of the covariance 
> matrix according to the covariate $Z$.
>  Thank you very much for your help,
>  Taki Shinohara
>  ----
>  Russell Shinohara, MSc
>  PhD Candidate and NIH Fellow
>  Department of Biostatistics
>  Bloomberg School of Public Health
>  The Johns Hopkins University
>  615 N. Wolfe St., Suite E3033
>  Baltimore, MD 21205
>  tel: (203) 499-8480
>  ______________________________________________
>  R-help at r-project.org mailing list
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.

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