Global Optimization Of The Simplex Algorithm

Lipschitz optimization is an important branch of global optimization. Global optimization algorithm of Lipschitz function is studied in this paper, the technology of the radial subdivision and bisection is used in simplex algorithms of global optimization. And the convergence of the algorithms is also proved. The main work is as follows:The development of the global optimization theory, research status, essential knowledge and the properties of the algorithms are introduced in the first chapterThe simplex algorithm with the bisection subdivision technology is introduced in the second chapter. The feasibility and the convergence of the algorithm are proved.In the third chapter, the simplex algorithm with the radial subdivision and bisection technology is developed, which took full use of the information of function value and combined with the branch and bound method. It is proved that the algorithm is executable and convergent. The numerical results is also given.In the last chapter, we studied the simplex algorithms with radial subdivision, discussed some properties of the subdivision, and then proved the convergence of the algorithms.