This book is an elegant and rigorous presentation of integer programming, exposing the subject's mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader's understanding and serving as a gateway to deeper study. Key topics include: * formulations* polyhedral theory* cutting planes* decomposition* enumeration* semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.
Michelangelo Conforti is Professor of Mathematics at the University of Padova. Together with G. Cornuejols and M. R. Rao, he received the 2000 Fulkerson Prize in discrete mathematics. Gerard Cornuejols is IBM University Professor of Operations Research at Carnegie Mellon University. His research has been recognized by numerous honors, among them the Fulkerson Prize, the Frederick W. Lanchester Prize, the Dantzig Prize, and the John von Neumann Theory Prize. Giacomo Zambelli is Associate Professor (Reader) of Management Science at the London School of Economics and Political Sciences. All three authors are leading experts in the fields of integer programming, graph theory, and combinatorial optimization.
Preface.- 1 Getting Started.- 2 Integer Programming Models.- 3 Linear Inequalities and Polyhedra.- 4 Perfect Formulations.- 5 Split and Gomory Inequalities.- 6 Intersection Cuts and Corner Polyhedra.- 7 Valid Inequalities for Structured Integer Programs.- 8 Reformulations and Relaxations.- 9 Enumeration.- 10 Semidefinite Bounds.- Bibliography.- Index.
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