Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
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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
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Journal ArticleDOI
Solving network manpower problems with side constraints
Wilson L. Price,Marc Gravel +1 more
TL;DR: In this paper, a number of methods of dealing with side constraints (those not included in the network formulation) are explored.
Journal ArticleDOI
The capacitated minimum spanning tree problem: On improved multistar constraints
TL;DR: The new test improves the performance of the lagrangean relaxation proposed in this paper for the random cost instances, and shows that the new inequalities are worth using for random cost and sparse instances.
Dissertation
High Performance Computing as a Combination of Machines and Methods and Programming
TL;DR: The document is organized into five chapters articulated around the main contributions, which depicts the landscape of supercomputers, comments the need for tremendous processing speed, and analyze the main trends in supercomputing.
Dissertation
On decomposition and piecewise linearization in petroleumproduction optimization
TL;DR: The motivation for this PhD research has been to attack this real time productionoptimization problem from a new angle which has many advantages with respect to finding the optimal operational strategy.
References
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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.