Package org.drip.optimization.cuttingplane

Class StrengthenedChvatalGomoryCut

java.lang.Object

org.drip.optimization.canonical.ILPConstraint

org.drip.optimization.cuttingplane.ChvatalGomoryCut

org.drip.optimization.cuttingplane.StrengthenedChvatalGomoryCut

All Implemented Interfaces:

LinearConstraint

public class StrengthenedChvatalGomoryCut
extends ChvatalGomoryCut

StrengthenedChvatalGomoryCut implements the Strengthened Chvatal Gomory 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
StrengthenedChvatalGomoryCut(int[][] aGrid, int[] bArray, double[] lambdaArray, int t)	StrengthenedChvatalGomoryCut Constructor

Method Summary

Modifier and Type	Method	Description
int	t()	Retrieve the Strengthening Integer
boolean	verify(int[] variateArray)	Verify if the Variate Array satisfies the Constraint

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

adjustedCoefficientArray, lambdaArray, unadjustedCoefficientArray

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

StrengthenedChvatalGomoryCut

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

StrengthenedChvatalGomoryCut Constructor

Parameters:

aGrid - "A" Constraint Grid

bArray - "b" Constraint Array

lambdaArray - The Lambda Array

t - Strengthening Integer

Throws:

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

Method Details

t

public int t()

Retrieve the Strengthening Integer

Returns:

The Strengthening Integer

verify

public boolean verify(int[] variateArray)
               throws java.lang.Exception

Verify if the Variate Array satisfies the Constraint

Overrides:

verify in class ChvatalGomoryCut

Parameters:

variateArray - The Input Variate Array

Returns:

TRUE - The Variate Array satisfies the Constraint

Throws:

java.lang.Exception - Thrown if the Verification cannot be done