Re: [R] constraint optimization: solving large scale general nonlinear problems
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)
constrx=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
Re: [R] constraint optimization: solving large scale general nonlinear problems
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)
constrx=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
generalnonlinear 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
[R] constraint optimization: solving large scale general nonlinear problems
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 (http://www.ziena.com/knitro.htm.) 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: http://maicanfg.googlepages.com/index.html 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 https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] constraint optimization: solving large scale general nonlinear problems
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 https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] constraint optimization: solving large scale general nonlinear problems
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. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] constraint optimization: solving large scale general nonlinear problems
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: http://maicanfg.googlepages.com/index.html
E-mail: florin.mai...@handels.gu.se
Not everything that counts can be
counted, and not everything that can be
counted counts.
--- Einstein ---
[[alternative HTML version deleted]]
__
R-help@r-project.org mailing list
https
Re: [R] constraint optimization: solving large scale general nonlinear problems
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
