I know that Matlab can solve this problem, but I didn't mention it in my
previous email since OP had asked for "native to R" solutions.
Ravi.
____________________________________________________________________
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
----- Original Message -----
From: Ravi Varadhan <rvarad...@jhmi.edu>
Date: Monday, March 1, 2010 2:27 pm
Subject: Re: [R] Advice wanted on using optim with both continuous and discrete
par arguments...
To: Uwe Ligges <lig...@statistik.tu-dortmund.de>
Cc: "r-help@r-project.org" <r-help@r-project.org>, Jeffrey Racine
<raci...@mcmaster.ca>
> Hi Uwe & Jeff,
>
> It seems to me that Jeff's problem falls under the class of
> "mixed-integer nonlinear programming" (MINLP) problem. I would
> classify this as a "damn tough optimization problem" (DTOP!). I am
> not sure if there is any R package that can handle this or there is
> any R link to a commercial package that can handle this (e.g. Rcplex).
> The optimzation task view only talks about MILP and MIQP
> (mixed-integer linear and quadratic programming).
>
> Being totally ignorant of the state-of-art methods for MINLP, I would
> like to suggest a "novel" approach for solving this:
>
> Let f(X,Y) be the objective function where X and Y be the continuous
> and categorical variables. You already have constraints g(X) on X.
> Now, let us treat Y as continuous. Let us define some artificial
> constraints on Y. For example, if we have only one variable y, let us
> define a constraint function that penalizes y as it gets away from
> integer values I = {0, 1, ..., K}, call this h(y; I, \sigma). This
> function is defined such that it is zero on the integer set I, but
> increases monotonically as a function of the distance away from the
> integer points. The parameter \sigma is like a scaling parameter. It
> should be relatively easy to come up with a smooth penalty function
> (may be some kind of a K-sum of reciprocal of Gaussian densities).
> You can then solve the resulting nonlinear programming problem for a
> sequence of \sigma values starting with a large dispersion and then
> decreasing it towards zero. You could use extrapolation to
> extrapolate to the limit as \sigma goes
> to zero. Of course, you will then round-off the solution at the end.
> Does this make sense?
>
> Ravi.
>
> ____________________________________________________________________
>
> Ravi Varadhan, Ph.D.
> Assistant Professor,
> Division of Geriatric Medicine and Gerontology
> School of Medicine
> Johns Hopkins University
>
> Ph. (410) 502-2619
> email: rvarad...@jhmi.edu
>
>
> ----- Original Message -----
> From: Uwe Ligges <lig...@statistik.tu-dortmund.de>
> Date: Monday, March 1, 2010 12:59 pm
> Subject: Re: [R] Advice wanted on using optim with both continuous
> and discrete par arguments...
> To: Jeffrey Racine <raci...@mcmaster.ca>
> Cc: "r-help@r-project.org" <r-help@r-project.org>
>
>
> >
> > On 01.03.2010 18:34, Jeffrey Racine wrote:
> > > Thanks Uwe.
> > >
> > > I appreciate your feedback.. in the paragraph in my email
> beginning
> > "The problem..."
> >
> > Whoops, apologies, I was too quickly reading your message, apparently.
> > CCing R-help to add:
> >
> > There is the Optimization Task View on CRAN:
> >
> >
> > See particularly the hints related to Mixed integer programming
> and
> > its
> > variants
> >
> > Best wishes,
> > uwe
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > > I point out that yes, I indeed do what you suggest for small
> > problems, but encounter problems where this is not feasible (e.g.,
> 10
> >
> > variables with integer ranging from 0-20 for each variable for instance).
> > >
> > > Thanks again!
> > >
> > > -- Jeff
> > >
> > > On 2010-03-01, at 12:28 PM, Uwe Ligges wrote:
> > >
> > >>
> > >>
> > >> On 01.03.2010 16:34, Jeffrey Racine wrote:
> > >>> Dear R users,
> > >>>
> > >>> I have a problem for which my objective function depends on
> both
> > discrete and continuous arguments.
> > >>>
> > >>> The problem is that the number of combinations for the
> > (multivariate) discrete arguments can become overwhelming (when it
> is
> > univariate this is not an issue) hence search over the continuous
> > arguments for each possible combination of the discrete arguments
> may
> > not be feasible. Guided search over the discrete and continuous
> > arguments would be infinitely preferable. That is, exhaustive
> search
> > over all possible combinations works perfectly, but for large
> problems
> > exhaustive search simply is not in the feasible set.
> > >>>
> > >>> Both the discrete and continuous arguments are bounded (the
> > discrete lie in [0,K] and the continuous in [0,1]) and I am using
> > L-BFGS-B with lower and upper vectors defining these bounds.
> > >>>
> > >>> The issue is that when I feed optim my objective function and
> par
> > (whose first `k' elements must necessarily be rounded by my
> objective
> > function while the remaining `l' arguments are continuous), the
> > default settings naturally do not perform well at all. Typically if
>
> > the initial values for the discrete variables are, say, par[1:3]=
> > c(2,3,4) while those for the continuous are, say, par[4:6] = c(.17,
>
> > .35, .85), then optim finds the minimum for only the continuous
> > variables and dumps back the initial values for the discrete
> > variables. I presume that the numerical approximation to the
> > gradients/hessian is thrown off by the `flat spots' or
> > step-like-nature of the objective function with respect to the
> > discrete variables.
> > >>>
> > >>> I have played with ndeps, parscale etc. but nothing really
> works.
> > I realize this is a mixed combinatorial optimization/continuous
> > optimization problem and ideally would love pointers to any related
>
> > literature or ideally an R package that implements such a beast.
> > >>>
> > >>> However, if anyone has attempted to use optimization routines
>
> > native to R with any success in similar settings, I would love to
> get
> > your feedback.
> > >>
> > >>
> > >> If your 3 first discrete variables have a rather limited number
> of
> > possible values (sounds like that is the case), you may want to
> apply
> > optim() on the other variables on a complete grid of the first 3
> > variables and select the best result. Even with this complete
> > evaluation of the whole grid with say 20 possible values in each
> > dimension the results should be there within minutes without a need
>
> > for more specialized optimization procedures. ...
> > >>
> > >> Best wishes,
> > >> Uwe Ligges
> > >>
> > >>
> > >>
> > >>> Many thanks in advance for your advice.
> > >>>
> > >>> -- Jeff
> > >>>
> > >>>
> > >>>
> > >>> Professor J. S. Racine Phone: (905) 525 9140 x 23825
> > >>> Department of Economics FAX: (905) 521-8232
> > >>> McMaster University e-mail: raci...@mcmaster.ca
> > >>> 1280 Main St. W.,Hamilton, URL:
> > >>> Ontario, Canada. L8S 4M4
> > >>>
> > >>> `The generation of random numbers is too important to be left
> to
> > chance'
> > >>>
> > >>> ______________________________________________
> > >>> R-help@r-project.org mailing list
> > >>>
> > >>> PLEASE do read the posting guide
> > >>> and provide commented, minimal, self-contained, reproducible code.
> > >
> > > Professor J. S. Racine Phone: (905) 525 9140 x 23825
> > > Department of Economics FAX: (905) 521-8232
> > > McMaster University e-mail: raci...@mcmaster.ca
> > > 1280 Main St. W.,Hamilton, URL:
> > > Ontario, Canada. L8S 4M4
> > >
> > > `The generation of random numbers is too important to be left to
> chance'
> > >
> > >
> > >
> > >
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> >
> > PLEASE do read the posting guide
> > and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help@r-project.org mailing list
>
> PLEASE do read the posting guide
> and provide commented, minimal, self-contained, reproducible code.
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