Review of the book
This book is a survey of non-linear integer programming in a general format. In this book, innovations in this field are given for those interested in computer science, operations research and optimization. In this book, an attempt has been made to express the solution order for nonlinear programming problems in addition to the theory.
Table of Contents
The topics discussed in this book are as follows:
1- Duality theory for nonlinear integer programming: In this section, the relationship between the duality gap and the disturbance function is expressed, which leads to a new theory for nonlinear programming. Based on this theory, the solution method for nonlinear integer programming is expressed.
2- The release method and cutting planes are used for separable non-linear integer programming. In this section, the necessary conditions for zeroing the matching gap to reach the optimal solution are stated.
3- Convexity is provided for non-convex integer programming and then the branch and bound method is changed based on convexity.
4- Using the descending iterative process to reach the global optimal solution in cases where the problem leads to the local optimal solution in the form of non-convex programming.
5- The use of solution methods for non-linear integer programming problems is examined in this book in large-scale problems.