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.