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 <rvaradhan at 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: rvaradhan at jhmi.edu
>
>
> ----- Original Message -----
> From: Florin Maican <florin.maican at 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
> <rvaradhan at jhmi.edu> Cc: r-help <r-help at 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
> > <rvaradhan at jhmi.edu> wrote:
> > > Hi,
> > >
> > > Looking at your problem, it seems like you can simply transform
> > > it
> > > 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: rvaradhan at jhmi.edu
> > >
> > >
> > > ----- Original Message -----
> > > From: Ravi Varadhan <rvaradhan at 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.maican at handels.gu.se>
> > > Cc: r-help <r-help at 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: rvaradhan at jhmi.edu
> > > >
> > > >
> > > > ----- Original Message -----
> > > > From: Florin Maican <florin.maican at 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 at r-project.org>
> > > >
> > > >
> > > > > Hi
> > > > >
> > > > > I need advice regarding constraint optimization with large
> > > > > number
> > > > > 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
> > > > > case. I need to solve this problem with over 300
> > > > > variables. In
> > > > > 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.maican at handels.gu.se
> > > > > ------------------------------------
> > > > > "Not everything that counts can be
> > > > > counted, and not everything that can be
> > > > > counted counts."
> > > > > --- Einstein ---
> > > > >
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> > > > >
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