symmetric matrix optimization

• May 26th 2009, 07:07 AM
Min.Lu
symmetric matrix optimization
Hi,guys:

We meet with an integer optimization defined as follows:

$v^{*} = argmax \quad
\frac{v^{T}X^{T}\left(\sum_{j=1}^{m}{b_iw_i^{T}}\r ight)Xv}{\sqrt{v^{T}X^{T}Xv}}
$

Where v denotes $n$ dimensional column parameter vector,
the domain of which is all permutations of $\left\{{1-n,2-n,
\ldots,2i-n-1,\ldots,n-1}\right\}$
. The entries matrix $X
\in \mathcal{R}^{n \times s}$
are known. $b_i,w_i$
are $n$ dimensional column vector.

Our Goal

Design a polynomial order algorithm to solve this problem.