**Review of the book**

This book is about the mathematics of discrete optimization, which includes modeling and its solution method. In part 1, the formulation of integer programming problems, the solution method and the relevant theory, which are needed in parts 2 and 3, are stated. In part 1, the things that are stated include linear programming, graph and network, complexity theory, multimodal theory and the solution statement for the linear programming model.

In sections 2 and 3, basic approaches for solving integer programming are described. In part 2, the things that are stated are: finding possible integer solutions from solving linear inequalities and making superadditive cuts, using liberation and congeneric theory in solving problems of correct solutions, the branch and edge method and the method of cutting planes, the initial method – We discuss the cognate finder, decomposition method, the application of the zero and one programming method, the traveling salesman problem and the fixed cost network problem. In part 3, the focus is on solving the combined optimization problems and their modeling.

This book can be used as a self-study book or a textbook for graduate level.

**Table of Contents**

Integer optimization and combinatorial optimization

linear programming

Network and graph

Multimodal theory

Computational complexity

Algorithms with polynomial solution time for linear programming

Integer grid

Valid inequality theory

Valid inequalities for structured integer models

Duality and relaxation

General algorithms

Algorithms with special applications

Integer polyhedra

Matching problem

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