Generalized Lagrange Multipliers (Classic Reprint): In Integer Programming: In Integer Programming (Classic Reprint) - Softcover

Shapiro, Jeremy F.

 
9780365653820: Generalized Lagrange Multipliers (Classic Reprint): In Integer Programming: In Integer Programming (Classic Reprint)

Synopsis

This book explores a novel approach to solving integer programming problems, a type of optimization problem that arises in many real-world applications. The author introduces a group-theoretic reformulation of integer programming, providing a new perspective on these complex problems. By constructing a Lagrangian problem, the author demonstrates how to find optimal or near-optimal solutions to integer programming problems, offering a valuable tool for researchers and practitioners alike. The book delves into the theoretical underpinnings of the approach, discussing necessary and sufficient conditions for optimality and exploring the relationship between the Lagrangian method and existing cutting-plane techniques. Through numerical examples, the author illustrates the practical application of the proposed methods. The book's insights advance the field of integer programming, providing a deeper understanding of these problems and opening up new avenues for further research.

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