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

Where denotes dimensional column parameter vector, each entry takes the integer and is defined as:

represents the optimal solution. denote dimensional column vector, whose values are known. The scalars are also defined.

Our 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.

This problem comes from my research, which is very important for me.

I hope you give me some suggestion and advice.

Thank you.