Package org.drip.optimization.cuttingplane

Class LetchfordLodiCut

java.lang.Object

org.drip.optimization.canonical.ILPConstraint

org.drip.optimization.cuttingplane.ChvatalGomoryCut

org.drip.optimization.cuttingplane.LetchfordLodiCut

All Implemented Interfaces:

LinearConstraint

public class LetchfordLodiCut
extends ChvatalGomoryCut

LetchfordLodiCut implements the Letchford-Lodi Cut for ILP. The References are:

• Burdet, C. A., and E. L. Johnson (1977): A Sub-additive Approach to Solve Linear Integer Programs Annals of Discrete Mathematics 1 117-143
• Chvatal, V. (1973): Edmonds Polytopes in a Hierarchy of Combinatorial Problems Discrete Mathematics 4 (4) 305-337
• Gomory, R. E. (1958): Outline of an Algorithm for Integer Solutions to Linear Programs Bulletin of the American Mathematical Society 64 (5) 275-278
• Kelley, J. E. (1960): The Cutting Plane Method for Solving Convex Problems Journal for the Society of the Industrial and Applied Mathematics 8 (4) 703-712
• Letchford, A. N. and A. Lodi (2002): Strengthening Chvatal-Gomory Cuts and Gomory Fractional Cuts Operations Research Letters 30 (2) 74-82

• Module = Computational Core Module
• Library = Numerical Optimizer Library
• Project = Necessary, Sufficient, and Regularity Checks for Gradient Descent and LP/MILP/MINLP Schemes
• Package = Polyhedral Cutting Plane Generation Schemes

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
LetchfordLodiCut(int[][] aGrid, int[] bArray, double[] lambdaArray)	ILPLetchfordLodiCut Constructor

Method Summary

Modifier and Type	Method	Description
double[]	adjustedCoefficientArray()	Generate the Adjusted Coefficient Array
LetchfordLodiPartitionMap	partitionMap()	Generate the Partition Map

Methods inherited from class org.drip.optimization.cuttingplane.ChvatalGomoryCut

lambdaArray, unadjustedCoefficientArray, verify

Methods inherited from class org.drip.optimization.canonical.ILPConstraint

aGrid, bArray, burdetJohnsonCut, chvatalGomoryCut, constraintCount, dimension, strengthenedBurdetJohnsonCut, strengthenedChvatalGomoryCut, validate

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

LetchfordLodiCut

public LetchfordLodiCut(int[][] aGrid,
int[] bArray,
double[] lambdaArray)
                 throws java.lang.Exception

ILPLetchfordLodiCut Constructor

Parameters:

aGrid - "A" Constraint Grid

bArray - "b" Constraint Array

lambdaArray - The Lambda Array

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

partitionMap

public LetchfordLodiPartitionMap partitionMap()

Generate the Partition Map

Returns:

The Partition Map

adjustedCoefficientArray

public double[] adjustedCoefficientArray()

Description copied from class: ChvatalGomoryCut

Generate the Adjusted Coefficient Array

Overrides:

adjustedCoefficientArray in class ChvatalGomoryCut

Returns:

The Adjusted Coefficient Array