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

Where denotes the dimensional column parameter vector, each entry taking the integer. represents the optimal solution. denotes the dimensional column vectors, the entries of which are known. denotes [tex]n-1[tex] dimensional integral column vector.

The Goal

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