Re: Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg35284] Re: [mg35273] Optimization*From*: Brett Champion <brettc at wolfram.com>*Date*: Sat, 6 Jul 2002 05:44:32 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On Fri, 5 Jul 2002, Etienne wrote: > Is there a Mathematica package that minimizes a constrained non-linear > function containing Min and Max. For example, f[x_,y_] := Min[ Cos[x-y] > Sin[2 x] Cos[y] - Cos[x y] , Cos[x]]. > Thanks in advance. NMinimize in Mathematica 4.2 will do this. In[1]:= <<NumericalMath`NMinimize` In[2]:= f[x_,y_]:=Min[Cos[x - y] Sin[2 x] Cos[y] - Cos[x y], Cos[x]] In[3]:= NMinimize[f[x,y],{x,y}] Out[3]= {-1.78936, {x -> -2.5056, y -> 0.0722398}} In[4]:= NMinimize[f[x,y], {x,y}, Method->"DifferentialEvolution"] Out[4]= {-1.84785, {x -> -0.668632, y -> -0.271995}} In[5]:= NMinimize[f[x,y],{x,y}, Method->{"NelderMead", RandomSeed->101}] Out[5]= {-1.84785, {x -> -0.668632, y -> -0.272001}} With the default method (NelderMead) NMinimize was trapped by a local minimum. DifferentialEvolution did much better, as did NelderMead with a non-default random seed. Looking at a contour plot of the function, this appears to be the correct minimum. Brett Champion