Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
Reads0
Chats0
TLDR
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8].Abstract:
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed.read more
Citations
More filters
Book ChapterDOI
An Integer Programming Test Problem Generator
Michael G. Chang,Fred Shepardson +1 more
TL;DR: This paper presents a methodology for evaluating new integer programming algorithms -- an area of mathematical programming which is not yet well understood and serves as a basis for discussion and further work.
Journal ArticleDOI
An efficient lagrangean relaxation scheme for linear and integer equal flow problems
TorjÖrn. Larson,Zhuangwei. Liu +1 more
TL;DR: In this paper, the Lagrangean dualization with respect to the equal flow side constraints and subgradient optimization are used to solve the original linear equal flow problem, which provides lower bounds on the optimal value of the original problem.
Proceedings ArticleDOI
Automatic decomposition of mixed integer programs for lagrangian relaxation using a multiobjective approach
TL;DR: This paper presents a new method to automatically decompose general Mixed Integer Programs (MIPs) by representing the constraint matrix for a general MIP problem as a hypergraph and relax constraints by removing hyperedges from the hypergraph.
Journal ArticleDOI
Extended cross decomposition for mixed-integer linear programs with strong and weak linking constraints
Emmanuel Ogbe,Xiang Li +1 more
TL;DR: This paper proposes a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, and extends a recently developed cross decomposition method based on this strategy to two-stage stochastic programming problems with conditional-value-at-risk constraints.
Journal ArticleDOI
Capital budgeting and lagrangian relaxation: A case study
TL;DR: In this article, a new approach to the classical multi-year capital budgeting problem is presented, arising out of an actual implementation of such a model, and three basic operational principles are specifically addressed in this approach.
References
More filters
Journal ArticleDOI
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
Journal ArticleDOI
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
TL;DR: The use of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions but can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set as mentioned in this paper.
Book ChapterDOI
Multicommodity Distribution System Design by Benders Decomposition
Arthur M. Geoffrion,G. W. Graves +1 more
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
Journal ArticleDOI
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.