Package org.drip.optimization.simplex

Class StandardForm

java.lang.Object

org.drip.optimization.simplex.StandardForm

All Implemented Interfaces:

DantzigSolver

public class StandardForm
extends java.lang.Object
implements DantzigSolver

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(ObjectiveFunction objectiveFunction, StandardPolytope constraintPolytope, boolean diagnosticsOn)	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
boolean	diagnosticsOn()	Retrieve the Diagnostics Setting
int	freeVariableCount()	Retrieve the Free Variable Count
PivotRun	multiPhaseOptimize()	Construct the Optimal Pivot Run Solution to the Simplex using a Multi-phase Optimizer
ObjectiveFunction	objectiveFunction()	Retrieve the Simplex Objective Function
PivotRun	phase1(boolean diagnosticsOn)	Perform the Phase 1 Simplex Run
boolean	phase2(PivotRun pivotRun)	Perform the Phase 2 Simplex Run - 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(ObjectiveFunction objectiveFunction,
StandardPolytope constraintPolytope,
boolean diagnosticsOn)
             throws java.lang.Exception

StandardForm Constructor

Parameters:

objectiveFunction - Objective Function

constraintPolytope - Constraint Polytope

diagnosticsOn - Diagnostics On Flag

Throws:

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

Method Details

objectiveFunction

public ObjectiveFunction 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

diagnosticsOn

public boolean diagnosticsOn()

Retrieve the Diagnostics Setting

Returns:

The Diagnostics Setting

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

basicFeasibleSolution

public double[] basicFeasibleSolution()

Compute the Basic Feasible Solution

Returns:

Basic Feasible Solution

phase1

public PivotRun phase1(boolean diagnosticsOn)

Perform the Phase 1 Simplex Run

Parameters:

diagnosticsOn - TRUE - Pivot Run Diagnostics Turned On

Returns:

The Phase 1 Pivot Run

phase2

public boolean phase2(PivotRun pivotRun)

Perform the Phase 2 Simplex Run - Process the Simplex Tableau to locate the Optimal Solution

Parameters:

pivotRun - The Pivot Run Instance

Returns:

TRUE - Phase 2 succeeded

multiPhaseOptimize

public PivotRun multiPhaseOptimize()

Construct the Optimal Pivot Run Solution to the Simplex using a Multi-phase Optimizer

Specified by:

multiPhaseOptimize in interface DantzigSolver

Returns:

The Optimal Pivot Run 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