New gradient methods for sensor selection problems

In this article, we consider the sensor selection problem of choosing T sensors from a set of m possible sensor measurements. The sensor selection problem is a combinational optimization problem. Evaluating the performance for each possible combination is impractical unless m and T are small. We relax the original selection problem to be a convex optimization problem and describe a projected gradient method with Barzilai–Borwein step size to solve the proposed relaxed problem. Numerical results demonstrate that the proposed algorithm converges faster than some classical algorithms. The solution obtained by the proposed algorithm is closer to the truth.