Filled Function Methods For Constrained Integer Programming Problems

This paper presents a new filled function method to solve constrained nonlinear integer programming problems with both inequality and equality constraints. In Chapter 1 we introduce significance of global optimization problem and one of the global optimization method, which is filled function method. We introduce the development of filled function method, purport of researching filled function method, some important filled functions, and results researched at home and abroad. In order to introduce the filled function method by the numbers to solve nonlinear integer programming problem, firstly we introduce the filled function method to solve box-constrained nonlinear integer programming problem proposed in [7] in Chapter 2. We also introduce some properties of the filled function, algorithm and numerical examples proposed in [7]. Then in Chapter 3 we introduce the filled function method involved this paper to solve nonlinear integer programming problem with inequality constraints proposed in [8]. Moreover, we introduce the properties of the filled function, algorithm and numerical examples proposed in [8].Chapter 4 is main results proposed in this paper, also is the shining point of this paper. Chapter 4 is organized by two parts chiefly. In first part, we propose a one-parameter filled function for the constrained integer programming problem with both inequality and equality constraints based on filled function methods proposed in [6] - [8], and some basic properties of the proposed filled function are discussed. In second part, a new global optimization method is proposed to obtain a discrete global minimizer of nonlinear integer programming problem with both inequality and equality constraints refered to algorithms proposed in [6] - [8]. Finally, an illustrative numerical example is given in this paper.