[R] Nonlinear constrains with optim

[Ravi Varadhan]

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.

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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

 

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-----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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