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

>

> ______________________________________________

>

[hidden email] 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:

[hidden email] Priv:

[hidden email]
______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.