scalation.maxima

ConjGradient

Related Doc: package maxima

class ConjGradient extends Error

Polak-Ribiere Conjugate Gradient (PR-CG) Algorithm for solving Non-Linear Programming (NLP) problems. PR-CG determines a search direction as a weighted combination of the steepest descent direction (-gradient) and the previous direction. The weighting is set by the beta function, which for this implementation used the Polak-Ribiere technique.

dir_k = -gradient (x) + beta * dir_k-1

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

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Instance Constructors

  1. new ConjGradient(f: FunctionV2S, g: FunctionV2S = null, ineq: Boolean = true)

    f

    the objective function to be maximized

    g

    the constraint function to be satisfied, if any

    ineq

    whether the constraint function must satisfy inequality or equality

Type Members

  1. type Pair = (VectorD, VectorD)

Value Members

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

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. final def asInstanceOf[T0]: T0

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  5. def beta(gr1: VectorD, gr2: VectorD): Double

    Compute the beta function using the Polak-Ribiere (PR) technique.

    Compute the beta function using the Polak-Ribiere (PR) technique. The function determines how much of the prior direction is mixed in with -gradient.

    gr1

    the gradient at the current point

    gr2

    the gradient at the next point

  6. def clone(): AnyRef

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  7. final def eq(arg0: AnyRef): Boolean

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  8. def equals(arg0: Any): Boolean

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  9. def fg(x: VectorD): Double

    The objective function f re-scaled by a weighted penalty, if constrained.

    The objective function f re-scaled by a weighted penalty, if constrained.

    x

    the coordinate values of the currrent point

  10. def finalize(): Unit

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  11. 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

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  12. final def getClass(): Class[_]

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  13. def hashCode(): Int

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  14. final def isInstanceOf[T0]: Boolean

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  15. def lineSearch(x: VectorD, dir: VectorD): Double

    Perform an inexact (e.g., WolfeLS) or exact (e.g., GoldenSectionLS) line search in the direction 'dir', returning the distance 'z' to move in that direction.

    Perform an inexact (e.g., WolfeLS) or exact (e.g., GoldenSectionLS) line search in the direction 'dir', returning the distance 'z' to move in that direction.

    x

    the current point

    dir

    the direction to move in

  16. final def ne(arg0: AnyRef): Boolean

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  17. final def notify(): Unit

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  18. final def notifyAll(): Unit

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  19. 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

  20. def setSteepest(): Unit

    Use the Steepest-Descent algorithm rather than the default PR-CG algorithm.

  21. def solve(x0: VectorD): VectorD

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

    Solve the following Non-Linear Programming (NLP) problem using PR-CG: max { 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

  22. final def synchronized[T0](arg0: ⇒ T0): T0

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  23. def toString(): String

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  24. final def wait(): Unit

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  25. final def wait(arg0: Long, arg1: Int): Unit

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  26. final def wait(arg0: Long): Unit

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