Dear Spencer, Thank you very much for your helpful reply. I was trying to reproduce a table in one paper. After I modified my code according to your suggestion, I was able to get the results that are very close to those in the paper. It seems the starting values of the parameters to be optimized are very crutial. So I will have different optimal values for different starting vectors. How can I be sure the min value returned by optim() is the true optimal value?
I am also curious why you choose the constant penalty to handle the constraint in the first place. Why not use lagrange multiplier method to eliminate the constraint? Thanks again. I am grateful for your help. Best regards, Iris On 7/18/06, Spencer Graves <[EMAIL PROTECTED]> wrote: > > I had good luck translating constrained into unconstrained > problems > and then optimizing the unconstrained problem. Have you tried something > like the following: > > Define: > z = c(z1, z2, z3), where p1=1/(1+exp(-z1), etc. This translates > the > constraints on the p's to > > G(z) = P*(f1(z)-r12*f2(z))^2-f1(z) > > where f1(z) = f1(p1(z1), p2(z2), p3(z3), and similarly for f2(z), and > where P = a penalty term, > and r12 = (1-c)*k1/(c*(1-k1). > > Can f2(z) ever go outside (0, 1)? If yes, I would modify G(z) by > adding a term like (min(0, f2(z), 1-f2(z))^2) > > If I haven't made a math error, your problem should translate > into > this form. I first solve this problem for z with P small like 1. Then > after I've got a solution for that, I increase P to 2, then 10, then > 100, etc., until the penalty is so great that the desired equality has > been effectively achieved. > > With 'P' fixed, 'optim' should handle this kind of problem > handily. > To learn how, I suggest you work through the examples in the ?optim help > page. I'd ignore the gradient, at least initially. A silly math error > in computing the gradient can delay a solutions unnecessarily. If you > need to solve thousands of problems like this for different values of > k1 and 'c', I might later program the gradient. However, I would not do > that initially. > > Also, if you are not already familiar with Venables and Ripley > (2002) > Modern Applied Statistics with S, 4th ed. (Springer -- or an earlier > edition), I would encourage you to spend some quality time with this > book. It can help you with 'optim', with contour plots, etc. > > Hope this helps, > Spencer Graves > > Iris Zhao wrote: > > Dear all, > > > > > > > > I am working on optimization problem and have some trouble running > optim(). > > I have two functions (f1, f2) and 4 unknown parameters (p1, p2, p3, p4). > > Both f1 and f2 are functions of p1, p2, and p3, denoted by f1(p1, p2, > p3) > > and f2(p1,p2,p3) respectively. > > > > > > > > The goal is to maximize f1(p1, p2, p3) subject to two constraints: > > > > (1) c = k1*p4/(k1*p4+(1-k1)*f1(p1,p2,p3)), where c and k1 are some > known > > constants > > > > (2) p4 = f2(p1, p2, p3) > > > > In addition, each parameter ranges from 0 to 1, and both f1 and f2 > involve > > integrations. > > > > > > > > I tried to use lagrange multipliers to eliminate two equality > constraints > > and then use optim() to find the maximum value and optimal parameter > > estimates. > > > > So I let fn be f1+lambda1*(c- k1*p4/(k1*p4+(1-k1)*f1(p1,p2,p3))) + > > lambda2(p4-f2(p1,p2,p3)). The error message I got was "Error in fn(par, > ...) > > : recursive default argument reference." > > > > > > > > I wonder whether current build-in functions in R can do this type of > jobs. > > Any suggestion will be greatly appreciated. > > > > > > > > Iris > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@stat.math.ethz.ch mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > [[alternative HTML version deleted]] ______________________________________________ R-help@stat.math.ethz.ch 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.
