A Point Within The Global Newton Optimization Algorithm

In this paper we describe an interior algorithm with global convergence of the general optimization problem. Considering the complementary action between Newton method and Penalty method, we define a merit function to simplify the selection of initial point, so that algorithm have excellent global behavior. The new merit function is good for global convergence and simplification algorithm without the penalty parameter.First, we describe some fundamental knowledge of the optimization. Such as, the framework of the optimization, the essential process of the algorithm.The second chapter, we describe some classical Interior-Methods. In recent years, many people studied the convergence of the Newton method and the Penalty method, and gave many different algorithm.Finally, we provide a Interior-Point Newton method with a new merit function basing on the classical Interior-point Newton methods, so that the step parameter a have different selection principle from other Interior-Point methods. In this chapter, we give the proof of the global convergence with standard conditions.