Foundations of Bilevel Programming

Review of the book
Bilevel programming problems were introduced in the optimization community in the 20th century. After that, the rapid development and intensive research of these problems in the theoretical and practical direction began. The ideas of mathematicians, economists and engineers and the number of articles in this field are growing rapidly. Two-level programming problems are of the hierarchical type, where there is a secondary optimization problem in the constraints. In two-level planning, the first level includes the internal problem and the second level includes the external problem. For example, on the internal level the behavior of nature is expressed and on the external level the main decision is made. From a mathematical point of view, two-level problems are among very complex problems (NP hard) and their solution is much more difficult and sometimes impossible compared to one-level problems.
Table of Contents
The topics discussed in this book are as follows:
1- Two-level programming applications
2- Linear two-level problems
3- Parametric optimization
4- Optimum conditions
5- Solving algorithms
6- Finding a solution using the interior method
7- Integer two-level problems