c

scalation.minima

QuasiNewton

class QuasiNewton extends Minimizer with Error

The QuasiNewton the class implements the 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: FunctionV2S, g: FunctionV2S = null, ineq: Boolean = true, exactLS: Boolean = false)

    f

    the objective function to be minimized

    g

    the constraint function to be satisfied, if any

    ineq

    whether the constraint is treated as inequality (default) or equality

    exactLS

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

Type Members

  1. type Pair = (VectorD, VectorD)
    Definition Classes
    Minimizer

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. val EPSILON: Double
    Attributes
    protected
    Definition Classes
    Minimizer
  5. val MAX_ITER: Int
    Attributes
    protected
    Definition Classes
    Minimizer
  6. val STEP: Double
    Attributes
    protected
    Definition Classes
    Minimizer
  7. val TOL: Double
    Attributes
    protected
    Definition Classes
    Minimizer
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  12. 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
    QuasiNewton → Minimizer
  13. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  15. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  16. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  17. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  18. 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
    QuasiNewton → Minimizer
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  22. def setDerivatives(partials: Array[FunctionV2S]): 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

  23. def setSteepest(): Unit

    Use the Gradient Descent algorithm rather than the default BFGS algorithm.

  24. def solve(x0: VectorD, step_: Double = STEP, toler: Double = TOL): 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 tolerance

    Definition Classes
    QuasiNewton → Minimizer
  25. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  26. def toString(): String
    Definition Classes
    AnyRef → Any
  27. 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

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

Inherited from Error

Inherited from Minimizer

Inherited from AnyRef

Inherited from Any

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