Re: [R] Optimization inconsistencies
peter dalgaard pdalgd at gmail.com writes: On May 18, 2012, at 00:14 , Nathan Stephens wrote: I have a very simple maximization problem where I'm solving for the vector x: objective function: w'x = value to maximize box constraints (for all elements of w): low x high equality constraint: sum(x) = 1 But I get inconsistent results depending on what starting values I. I've tried various packages but none seem to bee the very solver in Excel. Any recommendations on what packages or functions I should try? Use the equality constraint to reduce the dimension of the problem by one. Then formulate the inequality constraints and apply, e.g., constrOptim(). You can immediately write down and use the gradient, so method L-BFGS-B is appropriate. Because the problem is linear, there is only one maximum and no dependency on starting values. If you had supplied some data and code (which packages did you try, and how?), a more concrete answer would have been possible. My own test example worked out of the box. Hans Werner Sounds like a linear programming problem, so perhaps one of the packages that are specialized for that? lpSolve looks like it should do it. (As a general matter: There's nothing simple about constrained maximization problems, and generic optimizers aren't really geared towards dealing with large sets of constraints.) --Nathan __ 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] Optimization inconsistencies
Le 18/05/12 00:14, Nathan Stephens a écrit :
I have a very simple maximization problem where I'm solving for the vector
x:
objective function:
w'x = value to maximize
box constraints (for all elements of w):
low x high
equality constraint:
sum(x) = 1
But I get inconsistent results depending on what starting values I. I've
tried various packages but none seem to bee the very solver in Excel. Any
recommendations on what packages or functions I should try?
I had similar problem to solve (x were frequencies) and optimization
stops before to reach the global maximum. As hwborch...@googlemail.com
indicates, I fitted {x}-1 values because the last one is known by the
equality constraint.
For the vector constraints, I used w - -Inf when x goes out of the limits.
Finally I used Bayesian mcmc to get the convergence and it works much
better.
I don't know why in this case the optim does not converge.
Hope it hepls,
Marc
--
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Marc Girondot, Pr
Laboratoire Ecologie, Systématique et Evolution
Equipe de Conservation des Populations et des Communautés
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91405 Orsay Cedex, France
Tel: 33 1 (0)1.69.15.72.30 Fax: 33 1 (0)1.69.15.73.53
e-mail: marc.giron...@u-psud.fr
Web: http://www.ese.u-psud.fr/epc/conservation/Marc.html
Skype: girondot
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Re: [R] Optimization inconsistencies
On May 18, 2012, at 09:10 , Hans W Borchers wrote: peter dalgaard pdalgd at gmail.com writes: On May 18, 2012, at 00:14 , Nathan Stephens wrote: I have a very simple maximization problem where I'm solving for the vector x: objective function: w'x = value to maximize box constraints (for all elements of w): low x high equality constraint: sum(x) = 1 But I get inconsistent results depending on what starting values I. I've tried various packages but none seem to bee the very solver in Excel. Any recommendations on what packages or functions I should try? Use the equality constraint to reduce the dimension of the problem by one. Then formulate the inequality constraints and apply, e.g., constrOptim(). You can immediately write down and use the gradient, so method L-BFGS-B is appropriate. I considered making a similar remark, then realized that lpSolve actually allows equality constraints, so why not just use the tool that is designed for the job? Because the problem is linear, there is only one maximum and no dependency on starting values. However, with a linear objective function, the Hessian is 0 and the maximum is attained at a corner point, which is likely to confuse algorithms that expect a locally quadratic function. If you had supplied some data and code (which packages did you try, and how?), a more concrete answer would have been possible. My own test example worked out of the box. Yes, also from the development perspective. We need to see more of these hard examples. Hans Werner Sounds like a linear programming problem, so perhaps one of the packages that are specialized for that? lpSolve looks like it should do it. (As a general matter: There's nothing simple about constrained maximization problems, and generic optimizers aren't really geared towards dealing with large sets of constraints.) --Nathan __ 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd@cbs.dk Priv: pda...@gmail.com __ 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] Optimization inconsistencies
Marc Girondot marc_grt at yahoo.fr writes:
Le 18/05/12 00:14, Nathan Stephens a écrit :
I have a very simple maximization problem where I'm solving for the vector
But I get inconsistent results depending on what starting values I. I've
tried various packages but none seem to bee the very solver in Excel. Any
recommendations on what packages or functions I should try?
[...]
I had similar problem to solve (x were frequencies) and optimization
stops before to reach the global maximum. As [...] indicate[d], I fitted
{x}-1 values because the last one is known by the equality constraint.
For the vector constraints, I used w - -Inf when x goes out of the limits.
Same as before:
Would you *please* post data and code, as the posting guide requests!
The variable that is left out still has some (linear) inequalities to fullfil.
I didn't understand how you worked that out with optim() as it only allows to
include box constraints.
Hans Werner
Finally I used Bayesian mcmc to get the convergence and it works much
better.
I don't know why in this case the optim does not converge.
Hope it hepls,
Marc
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and provide commented, minimal, self-contained, reproducible code.
Re: [R] Optimization inconsistencies
On Thu, May 17, 2012 at 06:14:37PM -0400, Nathan Stephens wrote: I have a very simple maximization problem where I'm solving for the vector x: objective function: w'x = value to maximize box constraints (for all elements of w): low x high equality constraint: sum(x) = 1 Hi. As Peter Dalgaard suggested, lpSolve may be used. If low may contain negative values, then it is important to note that lpSolve assumes all variables nonnegative. So, a transformation is needed, for example x = low + y and solve for y. The following is one approach. library(lpSolve) n - 8 w - 1:n low - rep(-1, times=n) high - rep(1, times=n) crit - w mat - rbind(diag(n), 1) rhs - c(high - low, 1 - sum(low)) dir - c(rep(=, times=n), ==) out - lp(max, objective.in=crit, const.mat=mat, const.dir=dir, const.rhs=rhs) x - low + out$solution round(x, digits=15) [1] -1 -1 -1 0 1 1 1 1 Hope this helps. Petr Savicky. __ 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] Optimization inconsistencies
On May 18, 2012, at 00:14 , Nathan Stephens wrote: I have a very simple maximization problem where I'm solving for the vector x: objective function: w'x = value to maximize box constraints (for all elements of w): low x high equality constraint: sum(x) = 1 But I get inconsistent results depending on what starting values I. I've tried various packages but none seem to bee the very solver in Excel. Any recommendations on what packages or functions I should try? Sounds like a linear programming problem, so perhaps one of the packages that are specialized for that? lpSolve looks like it should do it. (As a general matter: There's nothing simple about constrained maximization problems, and generic optimizers aren't really geared towards dealing with large sets of constraints.) --Nathan [[alternative HTML version deleted]] __ 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd@cbs.dk Priv: pda...@gmail.com __ 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.
