A Coarse Idea

We meet with an integer optimizing problem, which is defined as follows:

Where denotes dimensional column parameter vector, each entry taking value from . represents the optimal solution. denote dimensional column vector, whose values are known. The matrix is defined on dimensional column vectors , where each column vector is definitively. The columns of are calculated by substraction of every two column vector . It is listed as follows:

The Goal

Our goal is to build an algorithm, which can solve the optimization problem in polynomial order time with , and . What's happiest, you can yield an analytical solution to the optimization problem.