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Integer Programming [Conforti] - mklabgr - 08-17-2026
Integer Programming
Authors: Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
Publication date: 2014
Publisher: Springer International Publishing
Series:Graduate Texts in Mathematics, Vol. 271
Integer Programming is a rigorous graduate-level introduction to optimization problems in which some or all variables are required to take integer values. Rather than treating integer programming simply as a collection of computational techniques, Conforti, Cornuéjols, and Zambelli emphasize the mathematical structures underlying modern algorithms. The book begins with basic formulations and modeling, introducing fundamental methods such as branch-and-bound and cutting planes, before developing the geometry of linear inequalities and polyhedra. This geometric viewpoint is central: integer optimization problems are studied through convex hulls, valid inequalities, and polyhedral descriptions that explain why modern algorithms work.
The later chapters move into considerably deeper territory, including perfect formulations, Gomory and split inequalities, intersection cuts, corner polyhedra, structured valid inequalities, reformulations and relaxations, enumeration methods, and semidefinite bounds. The authors balance formal theory with examples and exercises, while each chapter points readers toward further literature and specialized topics. This makes the book useful not only as a textbook but also as a bridge toward research in integer and combinatorial optimization. A major strength is the connection it establishes between abstract mathematical ideas—especially polyhedral geometry—and the techniques employed by practical optimization solvers.
The book is best suited to advanced undergraduate, graduate, or research-level readers with a solid background in linear algebra, discrete mathematics, and preferably linear programming. It is not primarily a beginner's "how to use an optimization package" manual; its goal is to explain the mathematics behind integer-programming methodology. For mathematically oriented readers interested in operations research, combinatorial optimization, algorithms, or discrete mathematics, it provides a particularly substantial introduction to the field.
Key takeaways
- Integer programming combines discrete mathematics, geometry, and algorithms: the polyhedral viewpoint provides much of the theoretical foundation.
- Cutting planes and branch-and-bound are fundamental: the book develops the mathematical reasoning behind techniques that underpin modern integer-programming solvers.
- The scope goes well beyond introductory optimization, reaching Gomory cuts, corner polyhedra, reformulations, enumeration, and semidefinite relaxations.
- Best for mathematically mature readers: it is especially valuable as a graduate textbook and as preparation for research in integer and combinatorial optimization.
Goodreads — Integer Programming