Development of Support Programs for Solving BMI Problems by Overbounding Approximation Method

A support program that implements the overbounding approximation method for MATLAB and YALMIP is developed. The overbounding approximation is one of the methods that provide sufficient LMI constraints for the given BMI constraints. With this method, one can obtain an approximate solution to the given BMI problem. However, it is not easy for ordinary users to implement the method to solve BMI problems. To overcome the difficulty, we provide a function that finds initial solutions for optimization and solves BMI problems automatically. This function enables users to obtain solutions for the BMI problem easily.