Help with constraints in a optimazation problem?

*To*: mathgroup at smc.vnet.net*Subject*: [mg60331] Help with constraints in a optimazation problem?*From*: jpahka at welho.com*Date*: Tue, 13 Sep 2005 06:07:14 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, The problem: I have a portfolio of around 250 equities. And I have daily returns for both the indivitual equities as well as the whole portfolio from around two years. And I'd like to replicate the return of the portfolio as closely as possible by using, say 20 equities. As a start I thought of using NMinimize to minimize tracking error (ie. sum of squares of the return difference) between this 20 equity portfolio and the original portfolio. So, I have the returns in a matrix so that the first column of the matrix is the return of the whole portfolio followed by the returns of the individual equities. Lets call this matrix as "ret". And I have a vector "weights" as the equity weights of the new portfolio. So, the function to minimize would be something like: func[ret_List, weights_List]:=Plus@@(((weights.Rest[#] - First[#])^2)&/@ret); subject to constraints: weights_i >= 0 ie. (# ≥ 0)& /@ weights Sum[weights] == 1 ie. Plus@@weights == 1 Max 20 weights_i > 0 This last one I don't know how to implement sanely. Surely I could use something like: Plus@@(Boole[# > 0.0001] &/@ weights) ≤ 20 but that's just too inefficient ( and ugly). Can anybody think of a better way of imposing such a constraint to this optimization promlem? Thanks in advance, Juhis