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 ...
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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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... 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.
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