Package org.drip.optimization.cuttingplane

Class StrengthenedBurdetJohnsonCut

java.lang.Object

org.drip.optimization.canonical.ILPConstraint

org.drip.optimization.cuttingplane.ChvatalGomoryCut

org.drip.optimization.cuttingplane.StrengthenedBurdetJohnsonCut

All Implemented Interfaces:

LinearConstraint

public class StrengthenedBurdetJohnsonCut
extends ChvatalGomoryCut

StrengthenedBurdetJohnsonCut implements the Strengthened Burdet-Johnson Cut for ILP. It provides the following Functions:

• StrengthenedBurdetJohnsonCut Constructor
• Retrieve the R¹ To R¹ Increasing Function
• Generate the Adjusted Coefficient Array

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
StrengthenedBurdetJohnsonCut(int[][] aGrid, int[] bArray, double[] lambdaArray, R1ToR1 increasingR1ToR1)	StrengthenedBurdetJohnsonCut Constructor

Method Summary

Modifier and Type	Method	Description
double[]	adjustedCoefficientArray()	Generate the Adjusted Coefficient Array
R1ToR1	increasingR1ToR1()	Retrieve the R1 To R1 Increasing Function

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

StrengthenedBurdetJohnsonCut

public StrengthenedBurdetJohnsonCut(int[][] aGrid,
int[] bArray,
double[] lambdaArray,
R1ToR1 increasingR1ToR1)
                             throws java.lang.Exception

StrengthenedBurdetJohnsonCut Constructor

Parameters:

aGrid - "A" Constraint Grid

bArray - "b" Constraint Array

lambdaArray - The Lambda Array

increasingR1ToR1 - R¹ To R¹ Increasing Function

Throws:

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

Method Details

increasingR1ToR1

public R1ToR1 increasingR1ToR1()

Retrieve the R¹ To R¹ Increasing Function

Returns:

The R¹ To R¹ Increasing Function

adjustedCoefficientArray

public double[] adjustedCoefficientArray()

Generate the Adjusted Coefficient Array

Overrides:

adjustedCoefficientArray in class ChvatalGomoryCut

Returns:

The Adjusted Coefficient Array