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Generalized Lagrange Multipliers (Classic Reprint): In Integer Programming: In Integer Programming (Classic Reprint) - Softcover
Synopsis
Explore a novel approach to solving integer programs with group theory and Lagrangian methods. This work shows how a reformulated problem can yield stronger, more practical solutions.
Built around a group-theoretic view of the integer programming problem, the book presents a Lagrangian formulation that aims to improve the combinatorial resolution of classic methods. It discusses how multipliers influence the search for good or optimal solutions and how cuts generated from this framework relate to traditional cutting planes. A practical, step-by-step development leads to a numerical example and remarks on extending the approach to zero-one problems.
The algebraic perspective is paired with an eye toward algorithmic use. The text connects the Lagrangian construction toCutting plane ideas and to the behavior of multipliers in guiding updates and bounds. It also addresses when and how the method can be a helpful heuristic, rather than a guaranteed solver, and how it complements existing group-theoretic techniques.
- Learn how to build a Lagrangian problem from an integer program using a group structure
- See how multipliers affect feasibility, bounds, and potential cuts
- Understand the relationship between Lagrangian cuts and strong cuts from cutting planes
- Review a numerical example that clarifies the method’s practical use
Ideal for readers seeking a rigorous yet accessible path to advanced optimization techniques, with an eye toward implementation in adaptive algorithms.
"synopsis" may belong to another edition of this title.
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Generalized Lagrange Multipliers: In Integer Programming (Classic Reprint)
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Paperback. Condition: New. Print on Demand. 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. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9780365653820_0
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Generalized Lagrange Multipliers
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9780365653820
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