LPPrimalDualMethod (patrimoine de base SIRIUS 4.15 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.OptimizationRequestHandler
- - fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.AbstractLPOptimizationRequestHandler
  - - fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.LPPrimalDualMethod

```
public class LPPrimalDualMethod
extends AbstractLPOptimizationRequestHandler
```
Primal-dual interior-point method for LP problems in the form (1):
min(c) s.t.
G.x < h
A.x = b
lb <= x <= ub
If lower and/or upper bounds are not passed in, a default value is assigned on them, that is:
-)if the vector lb is not passed in, all the lower bounds are assumed to be equal to the value of the field minLBValue
-)if the vector ub is not passed in, all the upper bounds are assumed to be equal to the value of the field maxUBValue
The problem is first transformed in the standard form, then presolved and finally solved.
Note 1: avoid to set minLBValue or maxUBValue to fake unbounded values.

Since:

4.6

Author:

alberto trivellato (alberto.trivellato@gmail.com)

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, p. 609"

Field Summary

Fields
Modifier and Type Field and Description

static double DEFAULT_MAX_UPPER_BOUND
Default maximum upper bound

static double DEFAULT_MIN_LOWER_BOUND
Default minimum lower bound
- Fields inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.OptimizationRequestHandler
  dim, MAX_ITERATIONS, meq, mieq, request, response, SCALAR, successor

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_MAX_UPPER_BOUND` Default maximum upper bound
`static double`	`DEFAULT_MIN_LOWER_BOUND` Default minimum lower bound

Constructor Summary

Constructors
Constructor and Description
`LPPrimalDualMethod()` Constructor It sets the default minimum lower bound and maximum upper bound
`LPPrimalDualMethod(double minLBVal, double maxUBVal)` Constructor

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`protected double`	`getF0(RealVector x)` Objective function value at X.
`protected RealVector`	`getFi(RealVector x)` Inequality functions values at X.
`protected RealVector`	`getGradF0(RealVector x)` Objective function gradient at X.
`protected RealMatrix`	`getGradFi(RealVector x)` Inequality functions gradients values at X.
`protected RealMatrix`	`getHessF0(RealVector x)` Objective function hessian at X.
`RealMatrix[]`	`getHessFi(RealVector x)` Inequality functions hessians values at X.
`protected RealVector`	`getLb()` Return the lower bounds for the problem.
`protected RealVector`	`getUb()` Return the upper bounds for the problem.
`protected RealVector`	`gradFiStepX(RealVector stepX)` Computes the term Grad[fi].stepX
`protected RealMatrix`	`gradLSum(RealVector l, RealVector fiX)` Return the H matrix (that is diagonal).
`protected RealVector`	`gradSum(double t, RealVector fiX)` Calculates the second term of the first row of (11.55) "Convex Optimization".
`protected boolean`	`isInDomainF0(RealVector x)` Objective function domain.
`protected static boolean`	`isLbUnbounded(Double lb)` Is the lower bound unbounded?
`protected static boolean`	`isUbUnbounded(Double ub)` Is the upper bound unbounded?
`int`	`optimize()` Solves an LP in the form of: min(c) s.t.
`protected int`	`optimizePresolvedStandardLP()` Solves a presolved standard form LP problem in the form of min(c) s.t.
`protected int`	`optimizeStandardLP(int nOfSlackVariables)` Solves a standard form LP problem in the form of min(c) s.t.
`protected RealVector`	`rDual(RealVector gradF0X, RealVector l, RealVector v)`
`protected RealVector`	`rPri(RealVector x)` rPri := Ax - b
`void`	`setKKTSolver(AbstractKKTSolver kktSol)` Set the KTT solver

Methods inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.AbstractLPOptimizationRequestHandler
getC, getG, getH, getLPOptimizationRequest, getLPOptimizationResponse, getYlb, getYub, getZlb, getZub, setLPOptimizationRequest, setLPOptimizationResponse, setOptimizationRequest, setOptimizationResponse

Methods inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.OptimizationRequestHandler
checkCustomExitConditions, findEqFeasiblePoint, findEqFeasiblePoint2, forwardOptimizationRequest, getA, getAlpha, getAT, getB, getBeta, getDim, getF0, getFi, getInitialLagrangian, getInitialPoint, getInteriorPointMethod, getMaxIteration, getMeq, getMieq, getMu, getNotFeasibleInitialPoint, getOptimizationRequest, getOptimizationResponse, getTolerance, getToleranceFeas, getToleranceInnerStep, getToleranceKKT, isCheckKKTSolutionAccuracy, isCheckProgressConditions

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_MIN_LOWER_BOUND
```
public static final double DEFAULT_MIN_LOWER_BOUND
```
    Default minimum lower bound
    
    See Also:
    
    Constant Field Values
  - DEFAULT_MAX_UPPER_BOUND
```
public static final double DEFAULT_MAX_UPPER_BOUND
```
    Default maximum upper bound
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - LPPrimalDualMethod
```
public LPPrimalDualMethod()
```
    Constructor It sets the default minimum lower bound and maximum upper bound
  - LPPrimalDualMethod
```
public LPPrimalDualMethod(double minLBVal,
                          double maxUBVal)
```
    Constructor
    
    Parameters:
    
    minLBVal - minimum lower bound
    
    maxUBVal - maximum upper bound
- Method Detail
  - optimize
```
public int optimize()
             throws PatriusException
```
    Solves an LP in the form of: min(c) s.t. A.x = b G.x < h lb <= x <= ub
    
    Overrides:
    
    optimize in class OptimizationRequestHandler
    
    Returns:
    
    retCode
    
    Throws:
    
    PatriusException - if an error occurs
  - optimizeStandardLP
```
protected int optimizeStandardLP(int nOfSlackVariables)
                          throws PatriusException
```
    Solves a standard form LP problem in the form of min(c) s.t. A.x = b lb <= x <= ub
    
    Parameters:
    
    nOfSlackVariables - number of slack variables
    
    Returns:
    
    result
    
    Throws:
    
    PatriusException - if an error occurs
  - optimizePresolvedStandardLP
```
protected int optimizePresolvedStandardLP()
                                   throws PatriusException
```
    Solves a presolved standard form LP problem in the form of min(c) s.t. A.x = b lb <= x <= ub
    
    Returns:
    
    result
    
    Throws:
    
    PatriusException - if an error occurs
  - gradSum
```
protected RealVector gradSum(double t,
                             RealVector fiX)
```
    Calculates the second term of the first row of (11.55) "Convex Optimization".
    
    Parameters:
    
    t - value
    
    fiX - vector
    
    Returns:
    
    result
    
    See Also:
    
    "Convex Optimization, 11.55"
  - gradLSum
```
protected RealMatrix gradLSum(RealVector l,
                              RealVector fiX)
```
    Return the H matrix (that is diagonal). This is the third addendum of (11.56) of "Convex Optimization".
    
    Parameters:
    
    l - vector
    
    fiX - vector
    
    Returns:
    
    H matrix
    
    See Also:
    
    "Convex Optimization, 11.56"
  - gradFiStepX
```
protected RealVector gradFiStepX(RealVector stepX)
```
    Computes the term Grad[fi].stepX
    
    Parameters:
    
    stepX - vector
    
    Returns:
    
    result
  - rDual
```
protected RealVector rDual(RealVector gradF0X,
                           RealVector l,
                           RealVector v)
```
    Parameters:
    
    gradF0X - vector
    
    l - vector
    
    v - vector
    
    Returns:
    
    result
    
    See Also:
    
    "Convex Optimization, p. 610"
  - setKKTSolver
```
public void setKKTSolver(AbstractKKTSolver kktSol)
```
    Set the KTT solver
    
    Parameters:
    
    kktSol - ktt solver
  - getF0
```
protected double getF0(RealVector x)
```
    Objective function value at X. This is C.X
    
    Overrides:
    
    getF0 in class OptimizationRequestHandler
    
    Parameters:
    
    x - value
    
    Returns:
    
    objective function
  - getGradF0
```
protected RealVector getGradF0(RealVector x)
```
    Objective function gradient at X. This is C itself.
    
    Overrides:
    
    getGradF0 in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    gradient
  - getHessF0
```
protected RealMatrix getHessF0(RealVector x)
```
    Objective function hessian at X. Hessians are null for linear problems
    
    Overrides:
    
    getHessF0 in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    objective function
  - getFi
```
protected RealVector getFi(RealVector x)
```
    Inequality functions values at X. This is (-x+lb) for all bounded lb and (x-ub) for all bounded ub.
    
    Overrides:
    
    getFi in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    inequality functions values
  - getGradFi
```
protected RealMatrix getGradFi(RealVector x)
```
    Inequality functions gradients values at X. This is -1 for all bounded lb and 1 for all bounded ub, and it is returned in a 2-rows compressed format. GradFi are not used for LP
    
    Overrides:
    
    getGradFi in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    a 2xdim matrix, 1 row for the lower bounds and 1 row for the upper bounds gradients
  - getHessFi
```
public RealMatrix[] getHessFi(RealVector x)
```
    Inequality functions hessians values at X. Hessians are null for linear problems
    
    Overrides:
    
    getHessFi in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    inequality function
  - rPri
```
protected RealVector rPri(RealVector x)
```
    rPri := Ax - b
    
    Overrides:
    
    rPri in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    result
  - isInDomainF0
```
protected boolean isInDomainF0(RealVector x)
```
    Objective function domain.
    
    Overrides:
    
    isInDomainF0 in class OptimizationRequestHandler
    
    Parameters:
    
    x - vector
    
    Returns:
    
    true
  - getLb
```
protected RealVector getLb()
```
    Return the lower bounds for the problem. If the original lower bounds are null, the they are set to the value of minLBValue. Otherwise, any lower bound is limited to the value of minLBValue
    
    Overrides:
    
    getLb in class AbstractLPOptimizationRequestHandler
    
    Returns:
    
    lower bounds
  - getUb
```
protected RealVector getUb()
```
    Return the upper bounds for the problem. If the original upper bounds are null, the they are set to the value of maxUBValue. Otherwise, any upper bound is limited to the value of maxUBValue
    
    Overrides:
    
    getUb in class AbstractLPOptimizationRequestHandler
    
    Returns:
    
    upper bounds
  - isLbUnbounded
```
protected static boolean isLbUnbounded(Double lb)
```
    Is the lower bound unbounded?
    
    Parameters:
    
    lb - lower bound
    
    Returns:
    
    true/false
  - isUbUnbounded
```
protected static boolean isUbUnbounded(Double ub)
```
    Is the upper bound unbounded?
    
    Parameters:
    
    ub - upper bound
    
    Returns:
    
    true/false

Class LPPrimalDualMethod

Field Summary

Fields inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.OptimizationRequestHandler

Constructor Summary

Method Summary

Methods inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.AbstractLPOptimizationRequestHandler

Methods inherited from class fr.cnes.sirius.patrius.math.optim.joptimizer.optimizers.OptimizationRequestHandler

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_MIN_LOWER_BOUND

DEFAULT_MAX_UPPER_BOUND

Constructor Detail

LPPrimalDualMethod

LPPrimalDualMethod

Method Detail

optimize

optimizeStandardLP

optimizePresolvedStandardLP

gradSum

gradLSum

gradFiStepX

rDual

setKKTSolver

getF0

getGradF0

getHessF0

getFi

getGradFi

getHessFi

rPri

isInDomainF0

getLb

getUb

isLbUnbounded

isUbUnbounded