Re: maximization with array of constraints

*To*: mathgroup at smc.vnet.net*Subject*: [mg128393] [mg128393] Re: maximization with array of constraints*From*: Dana DeLouis <dana01 at me.com>*Date*: Fri, 12 Oct 2012 00:01:07 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

> . . . my data is an array with two columns and 100 rows, I would have 100 constraints. . . Hi. Just some fun food for thought. ;>) Your 2-variable linear constraints makes it a little special. If your data was all positive, you could reduce the workload of NMaximize to only 1 constraint. Assume your data was all positive, and the following list represented 100 rows. data = {{5,5},{5,6},{4,20}}; your 100 constraints would look like this: const = Thread[data.{x,y}>0] {5 x+5 y>0,5 x+6 y>0,4 x+20 y>0} Do a region plot of the above. RegionPlot[const,{x,-4,4},{y,-4,4},GridLines->Automatic] You would have a hundred lines, but as you can see, if x is positive also, there is only 1 line that needs to be considered. It's the one with the smallest absolute slope. Clear[a,x,b,y]; Reduce[a x+b y>0&&b>0,y,Reals] b>0&& y > -((a x)/b) So, y must be the largest of -a/b (largest of the negative values) -data[[All,1]] / data[[All,-1]] {-1,-(5/6),-(1/5)} {Min[%],Max[%]} {-1,-(1/5)} So, the largest of the numbers is =E2=88=921/5, so the last equation above is the only constraint one must add. 4 x+20 y>0 If your data had -x values, then you would just have to add the Min value above for an additional constraint. (See chart as to why it changes) 5 x+5 y>0 If you wanted to carry it further, and y had negative values, you would just add 2 more constraints. Reduce[a x+b y >0 && b<0,y,Reals] b<0 && y < -((a x)/b) = = = = = = = = = = HTH :>) =E2=80=A8Dana DeLouis =E2=80=A8= = = = = = = = = = On Thursday, September 27, 2012 2:14:09 AM UTC-5, Felipe wrote: > Hi, > > > > I am trying to maximize a function using NMaximize and I have a large list of constraints that I would like to write with a loop or as an array. > > > > It looks like the following: > > > > NMaximize[{myfunction[x,y] , x*mydata[[1,row,1]] + y*mydata[[1,row,2]] >0 }] > > > > and I want the restriction to be valid for the numbers in each row of the "mydata" array. That is, if mydata is an array with two columns and 100 rows, I would have 100 constraints, which are too many to enter manually. > > Can I write a loop for the constraints inside NMaximize ? Do you have some suggestion on how to write this? I was not able to find it in earlier posts. > > > > Thank you very much for your help > > Felipe