t

scalation.minima

Minimizer

trait Minimizer extends AnyRef

The Minimizer trait sets the pattern for optimization algorithms for solving Non-Linear Programming (NLP) problems of the form:

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

where f is the objective function to be minimized g is the constraint function to be satisfied, if any

Classes mixing in this trait must implement a function 'fg' that rolls the constraints into the objective functions as penalties for constraint violation, a one-dimensional Line Search (LS) algorithm 'lineSearch' and an iterative method (solve) that searches for improved solutions 'x'-vectors with lower objective function values (f(x)).

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Known Subclasses
ConjugateGradient, CoordinateDescent, GradientDescent, L_BFGS_B, NelderMeadSimplex, QuasiNewton, StochasticGradient
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Type Members

  1. type Pair = (VectorD, VectorD)

Abstract Value Members

  1. abstract def lineSearch(x: VectorD, dir: VectorD, step: Double = STEP): Double

    Perform an exact, e.g., 'GoldenSectionLS' or inexact, e.g., 'WolfeLS' line search.

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

    x

    the current point

    dir

    the direction to move in

    step

    the initial step size

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

    Solve the Non-Linear Programming (NLP) problem by starting at 'x0' and iteratively moving down in the search space to a minimal point.

    Solve the Non-Linear Programming (NLP) problem by starting at 'x0' and iteratively moving down in the search space to a minimal point.

    x0

    the starting point

    step

    the initial step size

    toler

    the tolerance

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  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. val EPSILON: Double
    Attributes
    protected
  5. val MAX_ITER: Int
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    protected
  6. val STEP: Double
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    protected
  7. val TOL: Double
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  8. final def asInstanceOf[T0]: T0
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  10. final def eq(arg0: AnyRef): Boolean
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  11. def equals(arg0: Any): Boolean
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  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'. Override for constrained optimization and ignore for unconstrained optimization.

    x

    the coordinate values of the current point

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  1. def finalize(): Unit
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