Re: FindMinimum

*To*: mathgroup at smc.vnet.net*Subject*: [mg22183] Re: [mg22112] FindMinimum*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 17 Feb 2000 01:24:18 -0500 (EST)*References*: <200002160734.CAA17847@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Johannes Ludsteck wrote: > > Dear Mathgroup Members, > I have to minimize a function which is continuous but not smooth. > Someone suggested to use the flexible polyhedron search method > by Nelder and Mead. > The FindMinimum[] function in Mathematica doesn't use this > method, but seems to do the job well if I force use of the secant > method by givind two starting points for each variable. > Since the features of FindMinimum are not documented very well, I > wonder whether FindMinimum guarantees to find at least a local > minimum in my case. > > In case you are interested in the function: > > Plus @@ Abs[y - max[Dot[x, b], 0]], > > where y is a vector, x a matrix and b a vector. b contains the > miminization arguments. > > Johannes Ludsteck > Centre for European Economic Research (ZEW) > Department of Labour Economics, > Human Resources and Social Policy > Phone (+49)(0)621/1235-157 > Fax (+49)(0)621/1235-225 > > P.O.Box 103443 > D-68034 Mannheim > GERMANY > > Email: ludsteck at zew.de The secant method will generally work fine in this situation. Alternatively you might provide an explicit Gradient->... to FindMinimum because it cannot compute this symbolically. Yet another alternative would be to minimize an L2 rather than L1 distance (if this is a reasonable thing to do for your problem) by summing squares rather than absolute values. Nelder-Mead is probably not the best approach given that it is a bit crude. That said, we have an optimization package in development that incorporates N-M as a method. I am hopeful that it will become a standard add-on package once we're done polishing it. Possibly we will also make it a method for FindMinimum, I'm not sure at this time. Daniel Lichtblau Wolfram Research

**References**:**FindMinimum***From:*"Johannes Ludsteck" <ludsteck@zew.de>