Global Minimum of Measure Function and Quasi-convex Function

In, Zheng etc present a mean method for solving global optimization problems, if the objective function f(x) is continuous, the global convergence of the mean method is proved. In this paper, if f(x) is measurable function and satisfies the measure Lipschitz condition, we will prove the global convergence of mean method for the global optimization problems. Furthermore, if f(x) is a quasi-convex function in a bounded closed set, the global convergence of the mean method is also discussed.