scalation.minima

QuasiNewton

class QuasiNewton extends Minimizer with Error

Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi-Newton Algorithm for solving Non-Linear Programming (NLP) problems. BFGS determines a search direction by deflecting the steepest descent direction vector (opposite the gradient) by multiplying it by a matrix that approximates the inverse Hessian. Note, this implementation may be set up to work with the matrix 'b' (approximate Hessian) or directly with the 'binv' matrix (the inverse of b).

minimize f(x) subject to g(x) <= 0 [ optionally g(x) == 0 ]

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Error, Minimizer, AnyRef, Any
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Instance Constructors

  1. new QuasiNewton(f: (VectorD) ⇒ Double, g: (VectorD) ⇒ Double = null, ineq: Boolean = true, exactLS: Boolean = false)

    f

    the objective function to be minimized

    g

    the constraint function to be satisfied, if any

    exactLS

    whether to use exact (e.g., GoldenLS) or inexact (e.g., WolfeLS) Line Search

Type Members

  1. type Pair = (VectorD, VectorD)

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any
  3. final def ##(): Int

    Definition Classes
    AnyRef → Any
  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any
  6. val EPSILON: Double

    Attributes
    protected
    Definition Classes
    Minimizer
  7. val MAX_ITER: Int

    Attributes
    protected
    Definition Classes
    Minimizer
  8. val STEP: Double

    Attributes
    protected
    Definition Classes
    Minimizer
  9. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  10. def clone(): AnyRef

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  11. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  13. def fg(x: VectorD): Double

    The objective function f plus a weighted penalty based on the constraint function g.

    The objective function f plus a weighted penalty based on the constraint function g.

    x

    the coordinate values of the current point

    Definition Classes
    QuasiNewtonMinimizer
  14. def finalize(): Unit

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  15. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  16. final def getClass(): java.lang.Class[_]

    Definition Classes
    AnyRef → Any
  17. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  18. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  19. def lineSearch(x: VectorD, dir: VectorD, step: Double = STEP): Double

    Perform an exact (GoldenSectionLS) or inexact (WolfeLS) Line Search.

    Perform an exact (GoldenSectionLS) or inexact (WolfeLS) Line Search. Search in direction 'dir', returning the distance 'z' to move in that direction. Default to

    x

    the current point

    dir

    the direction to move in

    step

    the initial step size

    Definition Classes
    QuasiNewtonMinimizer
  20. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  21. final def notify(): Unit

    Definition Classes
    AnyRef
  22. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  23. def setDerivatives(partials: Array[(VectorD) ⇒ Double]): Unit

    Set the partial derivative functions.

    Set the partial derivative functions. If these functions are available, they are more efficient and more accurate than estimating the values using difference quotients (the default approach).

    partials

    the array of partial derivative functions

  24. def setSteepest(): Unit

    Use the Steepest-Descent algorithm rather than the default BFGS algorithm.

  25. def solve(x0: VectorD, step: Double = STEP, toler: Double = EPSILON): VectorD

    Solve the following Non-Linear Programming (NLP) problem using BFGS: min { f(x) | g(x) <= 0 }.

    Solve the following Non-Linear Programming (NLP) problem using BFGS: min { f(x) | g(x) <= 0 }. To use explicit functions for gradient, replace 'gradient (fg, x._1 + s)' with 'gradientD (df, x._1 + s)'.

    x0

    the starting point

    step

    the initial step size

    toler

    the tolerence

    Definition Classes
    QuasiNewtonMinimizer
  26. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  27. def toString(): String

    Definition Classes
    AnyRef → Any
  28. def updateBinv(s: VectorD, y: VectorD): Unit

    Update the 'binv' matrix, which is used to deflect -gradient to a better search direction than steepest descent (-gradient).

    Update the 'binv' matrix, which is used to deflect -gradient to a better search direction than steepest descent (-gradient). Compute the 'binv' matrix directly using the Sherman–Morrison formula.

    s

    the step vector (next point - current point)

    y

    the difference in the gradients (next - current)

    See also

    http://en.wikipedia.org/wiki/BFGS_method

  29. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()
  30. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
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    @throws()
  31. final def wait(arg0: Long): Unit

    Definition Classes
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    @throws()

Inherited from Error

Inherited from Minimizer

Inherited from AnyRef

Inherited from Any