Nonlinear Integer Programming / by Duan Li, Xiaoling Sun.

Springer eBooks

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 0–1 Optimization -- Constrained Polynomial 0–1 Programming -- Two Level Methods for Constrained Polynomial 0–1 Programming -- Mixed-Integer Nonlinear Programming -- Global Descent Methods.

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. 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.

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