Generalized Lagrange Multipliers: In Integer Programming (Classic Reprint)

Jeremy F. Shapiro

ISBN 10: 0365653829 / ISBN 13: 9780365653820

Editore: Forgotten Books, 2018

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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. Codice articolo 9780365653820_0

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Titolo: Generalized Lagrange Multipliers: In Integer...

Casa editrice: Forgotten Books

Data di pubblicazione: 2018

Legatura: Paperback

Condizione: New

Tipologia articolo: print-on-demand item

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Excerpt from Generalized Lagrange Multipliers: In Integer Programming

Several authors have proposed generalized Lagrangian methods for finding good or Optimal solutions to integer programming problems. The capital budgeting problem of Lorie and Savage essentially the 0-1 multi-dimensional Knapsack problem, has received particular attention in this regard. In Nemhauser and Ullman prove the somewhat negative result that the approach of Everett [4] applied to the capital budgeting problem by Kaplan in [8] can yield an optimal solution only if there is an Optimal linear programming solution that is integer. In this paper, we use group theory to reformulate the integer programming problem, thereby obtaining a Lagrangian problem which appears to Offer greater combinatorial resolution than previous methods. Conversely, the usefulness Of the group theoretic approach is enhanced by the Lagrangian problem.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.