Nonlinear Integer Programming

It is not an exaggeration that much of what people devote in their hfe re solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.

A combination of both Integer Programming and Nonlinear Optimization. Therefore, it will be a powerful book that surveys the field and provides a state-of-the-art treatment of Nonlinear Integer Programming The first book available on the area. As the reviewers note, the authors have achieved considerable advances in recent years and the book will summarize the field and its most recent results The authors' English is excellent. The book is written at the level of graduate students and it will be accessible to a wide audience of researchers, students, and practitioners Includes supplementary material: sn.pub/extras

Klappentext

It is not an exaggeration that much of what people devote in their hfe re­ solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve­ ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro­ gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.

Inhalt
Optimality, Relaxation and General Solution Procedures.- Lagrangian Duality Theory.- Surrogate Duality Theory.- Nonlinear Lagrangian and Strong Duality.- Nonlinear Knapsack Problems.- Separable Integer Programming.- Nonlinear Integer Programming with a Quadratic Objective Function.- Nonseparable Integer Programming.- Unconstrained Polynomial 01 Optimization.- Constrained Polynomial 01 Programming.- Two Level Methods for Constrained Polynomial 01 Programming.- Mixed-Integer Nonlinear Programming.- Global Descent Methods.