Package org.drip.optimization.simplex

Class StandardForm

java.lang.Object

org.drip.optimization.simplex.StandardForm

public class StandardForm
extends java.lang.Object

StandardForm exposes the Standard Form of the Simplex Scheme. The References are:

• Dadush, D., and S. Huiberts (2020): A Friendly Smoothed Analysis of the Simplex Method SIAM Journal on Computing 49 (5) 449-499
• Dantzig, G. B., and M. N. Thapa (1997): Linear Programming 1: Introduction Springer-Verlag New York NY
• Murty, K. G. (1983): Linear Programming John Wiley and Sons New York NY
• Nering, E. D., and A. W. Tucker (1993): Linear Programs and Related Problems Academic Press Cambridge MA
• Padberg, M. (1999): Linear Optimization and Extensions 2^nd Edition Springer-Verlag New York NY

• Module = Computational Core Module
• Library = Numerical Optimizer Library
• Project = Necessary, Sufficient, and Regularity Checks for Gradient Descent in a Constrained Optimization Setup
• Package = R^d to R¹ Simplex Scheme

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
StandardForm(LinearExpression objectiveFunction, StandardPolytope constraintPolytope)	StandardForm Constructor

Method Summary

Modifier and Type	Method	Description
double[]	basicFeasibleSolution()	Compute the Basic Feasible Solution
int	basicVariableCount()	Retrieve the Basic Variable Count
StandardPolytope	constraintPolytope()	Retrieve the Simplex Standard Constraint Polytope
int	freeVariableCount()	Retrieve the Free Variable Count
LinearExpression	objectiveFunction()	Retrieve the Simplex Objective Function
PivotRun	processTableau(boolean diagnosticsOn)	Process the Simplex Tableau to locate the Optimal Solution
int	slackVariableCount()	Retrieve the Slack Variable Count
double[][]	tableau()	Construct the Full Tableau
double[][]	tableauA()	Construct the Tableau A
double[]	tableauB()	Construct the Tableau B
double[]	tableauC()	Construct the Tableau C
java.lang.String	toString()	Convert the Standard Form into a String

Methods inherited from class java.lang.Object

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

Constructor Details

StandardForm

public StandardForm(LinearExpression objectiveFunction,
StandardPolytope constraintPolytope)
             throws java.lang.Exception

StandardForm Constructor

Parameters:

objectiveFunction - Objective Function

constraintPolytope - Constraint Polytope

Throws:

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

Method Details

objectiveFunction

public LinearExpression objectiveFunction()

Retrieve the Simplex Objective Function

Returns:

The Simplex Objective Function

constraintPolytope

public StandardPolytope constraintPolytope()

Retrieve the Simplex Standard Constraint Polytope

Returns:

The Simplex Standard Constraint Polytope

tableauA

public double[][] tableauA()

Construct the Tableau A

Returns:

Tableau A

tableauB

public double[] tableauB()

Construct the Tableau B

Returns:

Tableau B

basicVariableCount

public int basicVariableCount()

Retrieve the Basic Variable Count

Returns:

Basic Variable Count

freeVariableCount

public int freeVariableCount()

Retrieve the Free Variable Count

Returns:

Free Variable Count

slackVariableCount

public int slackVariableCount()

Retrieve the Slack Variable Count

Returns:

Slack Variable Count

tableauC

public double[] tableauC()

Construct the Tableau C

Returns:

Tableau C

tableau

public double[][] tableau()

Construct the Full Tableau

Returns:

Full Tableau

processTableau

public PivotRun processTableau(boolean diagnosticsOn)

Process the Simplex Tableau to locate the Optimal Solution

Parameters:

diagnosticsOn - TRUE - Pivot Run Diagnostics Turned On

Returns:

The Resulting Pivot Run

basicFeasibleSolution

public double[] basicFeasibleSolution()

Compute the Basic Feasible Solution

Returns:

Basic Feasible Solution

toString

public java.lang.String toString()

Convert the Standard Form into a String

Overrides:

toString in class java.lang.Object

Returns:

The Standard Form into a String