A feasible direction method for the semidefinite program with box constraints

In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible direction method. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, respectively. We establish the convergence of our algorithm, and report the numerical experiments which show the effectiveness of the algorithm.

► Solving the semidefinite program with box constraints has many important applications in engineering.
► We present a new algorithm for the box-constrained semidefinite program based on the feasible direction method.
► We establish the global convergence for the feasible direction algorithm for the semidefinite program with box constraints.