[R] ratio optimization with quadratic form

[Patrick Wang]

Hi, All

I have a function
f(y) = (x'Ax + 2yx'a_i+y^2*a_ii)/(x'Bx + 2yx'b_i+y^2*b_ii),

where A and B are known square matrix, a_i are the ith row of matrix A,
a_ii are the ith row/column element of matrix A.

what can I do to find a y to minize/maximize the ratio?

Do optimize function? can I do a matrix decomposition, a more elegant
solution?

Thanks
Pat