Nonlinear Integer Programming

Duan Li, Xiaoling Sun (auth.)0-387-29503-8, 0-387-32995-1, 978-0387-29503-9, 978-0387-32995-6

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.

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Table of contents :
Front Matter….Pages i-xxii
Introduction….Pages 1-11
Optimality, Relaxation and General Solution Procedures….Pages 13-44
Lagrangian Duality Theory….Pages 45-95
Surrogate Duality Theory….Pages 97-112
Nonlinear Lagrangian and Strong Duality….Pages 113-148
Nonlinear Knapsack Problems….Pages 149-207
Separable Integer Programming….Pages 209-239
Nonlinear Integer Programming with a Quadratic Objective Function….Pages 241-264
Nonseparable Integer Programming….Pages 265-291
Unconstrained Polynomial 0–1 Optimization….Pages 293-313
Constrained Polynomial 0–1 Programming….Pages 315-348
Two Level Methods for Constrained Polynomial 0–1 Programming….Pages 349-372
Mixed-Integer Nonlinear Programming….Pages 373-395
Global Descent Methods….Pages 397-417
Back Matter….Pages 419-437