The Lagrangian Relaxation Method for Solving Integer Programming Problems

By Marshall L. Fisher. Management Sciences, 2004

2,061 citations recorded by the source corpus.

Subfields: Industrial and Manufacturing Engineering, Numerical Analysis, Organizational Behavior and Human Resource Management

View Paper: https://www.semanticscholar.org/paper/fa52c5043af1b2046396c82f0e573084dcdc9d5e

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Citations in the corpus

Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach (2011, methodology): “By dualizing hard constraints to the objective function (Fisher, 1981), the Lagrangian relaxation method is a well-known solution procedure for integer programming problems.”
A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain (2012, methodology): “The Lagrangian multipliers lt are updated at each iteration using standard sub-gradient optimization (Fisher, 2004).”
Latency Minimization for Intelligent Reflecting Surface Aided Mobile Edge Computing (2019, neutral): “ˆ (cid:96) k ∈ [0 , L k ] is used to represent the relaxation [46] of the integer value (cid:96) k ∈ { 0 , 1 , . . . , L k } .”
A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing (2012, methodology): “See Lemar´echal (2001) and Fisher (1981) for surveys of LR methods, and Korte and Vygen (2008) for background on combinatorial optimization.”
Unit commitment by enhanced adaptive Lagrangian relaxation (2004, background): “The values of and are determined heuristically [ 23 ].”
Reliability Models for Facility Location: The Expected Failure Cost Case (2005, methodology): “For example, a given customer might receive 80% of its demand from its nearest facility, 15% from its second-nearest, and 5% from its thirdnearest. These percentages are inputs to the model. In our models, the “higher-level” assignments are only used when the primary facilities fail; there are no pr”
Reliable Facility Location Design Under the Risk of Disruptions (2010, methodology): “We use standard subgradient optimization technique to update the Lagrangian multipliers μ, as described in Fisher (18).”
An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results (2002, methodology): “We do so using a standard subgradient optimization procedure [15,16].”
Dynamic-demand capacitated facility location problems with and without relocation (2011, methodology): “The Lagrangian relaxation approach to solving mixed-integer programs (Fisher 1981 ) is well known with many applications in the facility location literature.”
Introduction to dual composition for inference (2011, methodology): “To remove these “complicating” constraints, we use the technique of Lagrangian relaxation (Geoffrion, 1974; Schlesinger, 1976; Fisher, 1981; Lemaréchal, 2001; Guignard, 2003).”