Can I get some advice about optimizing this algorithm?

vx2008 · Post by **vx2008** » Fri Feb 17, 2017 1:04 pm

Know values: matrix(n x m)—— X,F and Delta; vector—-u;

wanted value: vector—— w;

restrictive condition：

pic

Now shall I set vector — ‘w’ to get the biggest value of R/P?

Tradenator · Post by **Tradenator** » Fri Feb 17, 2017 1:17 pm

Is R correctly specified? You are trying to add a vector to a matrix multiplication?

vx2008 · Post by **vx2008** » Sat Feb 18, 2017 2:01 am

thanks for your reply;

Yes, I want to get a vector 'w' to make 'R/P' biggest.

ebal · Post by **ebal** » Tue Feb 21, 2017 2:59 pm

Seems like you simply have R = b w and P = sqrt(w^T C w). Their ratio is invariant to re-scaling of w, so you can always choose w so that P = 1. Then you have to maximize R with fixed P which is Lagrange optimization problem: b w + l (w^T C w - 1), where l is Lagrange multiplier (note P^2 to get rid of square root). This is straightforward.