Two Classes Of Filled Function For Constrained Global Optimization Problem

This paper mainly concerns nonlinear global optimization problems with filled function, which consists of five chapters.In the first chapter, we introduce the background of our research and main work on basis of some classical optimization problems as well as the development of filled function.The second chapter is the main body of this paper. On the one hand, the first class of filled function for constrained global optimization problems is constructed, and its properties are proved under several mild assumptions. On the other hand, the second class of filled function is proposed to avoid some limitations of the first class of filled function. Similarly, its properties are proved.In the third chapter, a class of discrete filled function is proposed based on the second class of continuous filled function. Then, the discrete properties of the filled function are presented.Two algorithms are designed according to the filled functions presented above. Additionally, the numerical results of several examples show that our algorithms are effective. Finally, we give the conclusions as well as some future research.