We meet with an integer optimization defined as follows:

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

Where v denotes n dimensional column parameter vector,
the domain of which is all permutations of \left\{{1-n,2-n,<br />
\ldots,2i-n-1,\ldots,n-1}\right\}. The entries matrix X<br />
\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.

Appreciate you very much for your suggestion and advice.