You don't need to find the fixed points. This is a kind of "profiling"
approach. As I had said before, a better approach would be to jointly maximize
over x and b:
max_{x, b} h(x, b) = f(g(x,b), b).
You can use any unconstrained optimization tools (assuming there are no
box-constraints on x and/or b) including optim() or spg() in the "BB" package.
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: Florin Maican <florin.mai...@handels.gu.se>
Date: Sunday, March 29, 2009 12:02 pm
Subject: Re: [R] constraint optimization: solving large scale general nonlinear
problems
To: Ravi Varadhan <rvarad...@jhmi.edu>
Cc: r-help <r-help@r-project.org>
> Ravi,
>
> I solve for the fixed-point x=g(x;b,Y). The variable Y is given - i
> can omitted here to not introduce confusion.
>
> max_{x,b} f(x,b)
>
> constr x=g(x;b)
>
> Let b1 the initial values for b. Having b1 I
> can compute the solution x1 of the system x=g(x,b1) - x1 fixed-point.
> So,
>
> b2= max_{b} f(x1,b)=f( g(x1,b),b), since x1=g(x1,b)
>
> I repeat this until || b_{n}-b_{n-1}||< eps then I have b optim.
>
> Why I introduce discontinuity in f?
> It is hard in this way to control the error from solving the
> fixed-point. In addition, the x=g(x,b) may have multiple solutions.
> For those reasons, I want to solve a constraint optimization
> problem.
>
> Best regards,
> Florin
>
>
> On Fri, 27 Mar 2009 18:03:02 -0400
> Ravi Varadhan <rvarad...@jhmi.edu> wrote:
>
> > Florin,
> >
> > How do you obtain x from (Y, b), i.e. x = g(Y,b)?
> >
> > I don't follow how a "discontinuity" is introduced, when you plug in
> > x(Y, b) into f. If f(.) is smooth and all the g(.) are smooth, then
> > the composition f(g(.)) will also be smooth. If this is not the
> > case, what type of discontinuity do you have (e.g. f(.) is
> > continuous, but its gradient is not, or f(.) itself has jump
> > discontinuites)?
> >
> > 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: Florin Maican <florin.mai...@handels.gu.se>
> > Date: Friday, March 27, 2009 3:48 pm
> > Subject: Re: [R] constraint optimization: solving large scale
> > general nonlinear problems To: Ravi Varadhan
> > <rvarad...@jhmi.edu> Cc: r-help <r-help@r-project.org>
> >
> >
> > > The number of variables is larger that the number of functions
> > > constraints. You are right I can rewrite my problem like this
> > >
> > > max f =h1(x11;x12;..;x1n;Y,b)+ h2(x21,x22, ... x2m;Y,b)
> > > x,b
> > >
> > > I know Y and for given values of b I can compute {x11,
> > > x1n} as
> > > one system of equations
> > > and {x21,x22 and x2m} as another system of equations. The x are
> > > functions of Y and b.
> > >
> > > I can solve these systems and after plug x(Y,b) in f(.) and
> > > find optimal b, but this will introduce discontinuity and I cannot
> > > find the optimal solution. I tried like this by using Rgenoud and
> > > SANN but both algorithms did not converge after 1 week!!!!!
> > > In my case the number of h functions are over 30.
> > >
> > > Florin
> > >
> > >
> > > On Fri, Mar 27, 2009 at 8:19 PM, Ravi Varadhan
> > > <rvarad...@jhmi.edu> wrote:
> > > > Hi,
> > > >
> > > > Looking at your problem, it seems like you can simply transform
> > > > it
> > > to an
> > > > unconstrained problem:
> > > >
> > > > Maximize h(x1, x2, ..., xn)
> > > >
> > > > where h(x1, x2, ..., xn) = f(g1(x), g2(x), ..., gn(x)).
> > > >
> > > > Am I missing something or haven't you provided all the
> > > > information?
> > > >
> > > > 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: Friday, March 27, 2009 2:42 pm
> > > > Subject: Re: [R] constraint optimization: solving large scale
> > > > general nonlinear problems
> > > > To: Florin Maican <florin.mai...@handels.gu.se>
> > > > Cc: r-help <r-help@r-project.org>
> > > >
> > > >
> > > > > Can you tell us more about your obj function, f, and the
> > > > > equality constraints g_k?
> > > > >
> > > > > Do you really have as many equality constraints as the number
> > > > > of variables? Are these all non-linear? Can't you find the
> > > > > roots of this system of equations? If yes, you could find all
> > > > > the roots (with multiple starts or some other search
> > > > > technique) and choose the one that maximizes f(x).
> > > > >
> > > > > 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: Florin Maican <florin.mai...@handels.gu.se>
> > > > > Date: Friday, March 27, 2009 2:01 pm
> > > > > Subject: [R] constraint optimization: solving large scale
> > > > > general nonlinear problems
> > > > > To: r-help <r-help@r-project.org>
> > > > >
> > > > >
> > > > > > Hi
> > > > > >
> > > > > > I need advice regarding constraint optimization with large
> > > > > > number
> > > > > of
> > > > > > variables.
> > > > > >
> > > > > > I need to solve the following problem
> > > > > >
> > > > > > max f(x1,...,xn)
> > > > > > x1,..xn
> > > > > >
> > > > > > x1=g1(x1,...,xn)
> > > > > > .
> > > > > > .
> > > > > > xn=gn(x1,...,xn)
> > > > > >
> > > > > > I am using Rdonlp2 package which works well until 40
> > > variables in
> > > > > my
> > > > > > case. I need to solve this problem with over 300
> > > > > > variables. In
> > > > > this case
> > > > > > Rdonlp2 is very very slowly. I know that in Matlab
> > > > > > exists Knitro ( for large optimization problems.
> > > > > >
> > > > > > It will be great if you can suggest me some alternatives
> > > > > > solutions.
> > > > > >
> > > > > >
> > > > > > Thanks in advance,
> > > > > > Florin
> > > > > >
> > > > > >
> > > > > >
> > > > > > --
> > > > > > Florin G. Maican
> > > > > > ==================================
> > > > > >
> > > > > > Ph.D. candidate,
> > > > > > Department of Economics,
> > > > > > School of Business, Economics and Law,
> > > > > > Gothenburg University, Sweden
> > > > > > -----------------------------------
> > > > > > P.O. Box 640 SE-405 30,
> > > > > > Gothenburg, Sweden
> > > > > >
> > > > > > Mobil: +46 76 235 3039
> > > > > > Phone: +46 31 786 4866
> > > > > > Fax: +46 31 786 4154
> > > > > > Home Page:
> > > > > > E-mail: florin.mai...@handels.gu.se
> > > > > > ------------------------------------
> > > > > > "Not everything that counts can be
> > > > > > counted, and not everything that can be
> > > > > > counted counts."
> > > > > > --- Einstein ---
> > > > > >
> > > > > > ______________________________________________
> > > > > > 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.
> > > >
> > > >
> > >
> > >
> > > --
> > > --
> > > Florin G. Maican
> > > ==================================
> > >
> > > Ph.D. candidate,
> > > Department of Economics,
> > > School of Business, Economics and Law,
> > > Gothenburg University, Sweden
> > > -----------------------------------
> > > P.O. Box 640 SE-405 30,
> > > Gothenburg, Sweden
> > >
> > > Mobil: +46 76 235 3039
> > > Phone: +46 31 786 4866
> > > Fax: +46 31 786 4154
> > > Home Page:
> > > E-mail: florin.mai...@handels.gu.se
> > > ------------------------------------
> > > "Not everything that counts can be
> > > counted, and not everything that can be
> > > counted counts."
> > > --- Einstein ---
> >
>
>
> --
> Florin G. Maican
> ==================================
>
> Ph.D. candidate,
> Department of Economics,
> School of Business, Economics and Law,
> Gothenburg University, Sweden
> -----------------------------------
> P.O. Box 640 SE-405 30,
> Gothenburg, Sweden
>
> Mobil: +46 76 235 3039
> Phone: +46 31 786 4866
> Fax: +46 31 786 4154
> Home Page:
> E-mail: florin.mai...@handels.gu.se
> ------------------------------------
> "Not everything that counts can be
> counted, and not everything that can be
> counted counts."
> --- Einstein ---
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