Ebook: 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.

The methodological development of integer programming has grown by leaps and bounds in the past four decades, with its main focus on linear integer programming. However, the past few years have also witnessed certain promising theoretical and methodological achievements in nonlinear integer programming. These recent developments have produced applications of nonlinear (mixed) integer programming across a variety of various areas of scientific computing, engineering, management science and operations research. Its prominent applications include, for examples, portfolio selection, capital budgeting, production planning, resource allocation, computer networks, reliability networks and chemical engineering.

In recognition of nonlinearity's academic significance in optimization and its importance in real world applications, NONLINEAR INTEGER PROGRAMMING is a comprehensive and systematic treatment of the methodology. The book's goal is to bring the state-of-the-art of the theoretical foundation and solution methods for nonlinear integer programming to students and researchers in optimization, operations research, and computer science. This book systemically investigates theory and solution methodologies for general nonlinear integer programming, and at the same time, provides a timely and comprehensive summary of the theoretical and algorithmic development in the last 30 years on this topic. The following are some features of the book: