(complicated) matrix differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg43358] (complicated) matrix differentiation
- From: "Eugene Salinas" <eugenesalinas2003 at yahoo.com>
- Date: Tue, 26 Aug 2003 07:13:32 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello everyone, I have to confess to being totally clueless re Mathematica so I am hoping for some nice guiding advice to help me solve my problem ... I'm writing an optimization routine and need to take derivatives (first and second) of the objective function. This isn't really my area so although I hope to do it analytically I would like to use the symbolic subroutines to verify my argument. Anyway, here is the problem: Objective function F(Y)=tr[(X'BX)^-1 X'AX] I need dF(Y) and ddF(Y). To get dF(Y) I used the implicit definition where tr[V'dF(Y)]=(d/dt)F(Y(t)) evaluated at t=0 for Y(t)=Y+tV. After some manipulations I get that dF(Y)=-2(BX(X'BX)^-1)X'AX(X'BX)^-1+2AX(X'BX)^-1 now I guess I could just take the straight forward derivatives with respect to X and it will be messy but presumably correct. Then I can use these in the numerical part. It's just that I'm not so sure of my matrix calculus and would like Mathematica to give it some added credibility. Any suggestions? Thanks a lot, Eugene.