Improvement of Convergence in the Successive Linearization Method for BMI Problems Using Freedom of the Convexification Term

The objective of this paper is to propose a method for improving the convergence rate of the successive linearization method for BMI problems. The successive linearization method is an iterative method in which a BMI constraint is reduced to a sufficient LMI constraint by adding a convexification term to the BMI term. In this method, the convexification term includes a constant matrix which is usually chosen as an identity matrix. The key idea of the proposed method is to make the convexification term “small” by an appropriate choice of the constant matrix, which is expected to lessen the conservativeness of the sufficiency of the LMI constraint.