Re: [R] Nonlinear constrains with optim

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Thu, 10 May 2007 14:48:16 -0400

Paul,

The general idea here is to transform a constrained problem into a sequence of unconstrained optimization problems. When only equality constraints are involved, a popular way to do this is to augment the objective function with a Lagrangian term and with a quadratic penalty term. When general inequalities are present, it is a lot harder, but various kinds of "barrier functions" are used.

A canonical reference (quite theoretical) for constrained optimization is the book:
Fiacco and McCormick (1968, but reprinted as classic by SIAM in 1990): Nonlinear programming: sequential unconstrained minimization techniques.

Another good book is that by Roger Fletcher (1987): Practical methods of optimization.

Ravi.



Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan_at_jhmi.edu

Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html  



-----Original Message-----
From: r-help-bounces_at_stat.math.ethz.ch
[mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of Paul Smith Sent: Thursday, May 10, 2007 11:08 AM
To: R-help
Subject: [R] Nonlinear constrains with optim

Dear All

I am dealing at the moment with optimization problems with nonlinear constraints. Regenoud is quite apt to solve that kind of problems, but the precision of the optimal values for the parameters is sometimes far from what I need. Optim seems to be more precise, but it can only accept box-constrained optimization problems. I read in the list archives that optim can also be used with nonlinear constrains through penalizations. However, I am not familiar with the technique of penalizations. Could someone please indicate to me a site or a book to learn about that penalization technique?

Thanks in advance,

Paul



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