c

scalation.minima

GoldenSectionLS

class GoldenSectionLS extends LineSearch

The GoldenSectionLS class performs a line search on 'f(x)' to find a minimal value for 'f'. It requires no derivatives and only one functional evaluation per iteration. A search is conducted from 'x1' (often 0) to 'xmax'. A guess for 'xmax' must be given, but can be made larger during the expansion phase, that occurs before the recursive golden section search is called. It works on scalar functions (see GoldenSectionLSTest). If starting with a vector function 'f(x)', simply define a new function 'g(y) = x0 + direction * y' (see GoldenSectionLSTest2).

Linear Supertypes
LineSearch, AnyRef, Any
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Instance Constructors

  1. new GoldenSectionLS(f: FunctionS2S, τ: Double = 1E-5)

    f

    the scalar objective function to minimize

    τ

    the tolerance for breaking the iterations

Value Members

  1. def gsection(left: Boolean, x1: Double, x2: Double, x3: Double, f2: Double): Double

    A recursive golden section search requiring only one functional evaluation per call.

    A recursive golden section search requiring only one functional evaluation per call. It works by comparing two center points x2 (given) and x4 computed.

    left

    whether to search left (true) or right (false) side of last interval

    x1

    the left-most point

    x2

    the center point (.618 across for left and .382 across for right)

    x3

    the right-most point

    f2

    the functional value for the x2 center point

  2. def lsearch(xmax: Double = 2.0, x1: Double = 0.0): Double

    Perform an exact Line Search (LS) using the Golden Search Algorithm.

    Perform an exact Line Search (LS) using the Golden Search Algorithm. Two phases are used: an expansion phase (moving the end-point) to find a down-up pattern, followed by a traditional golden section search.

    xmax

    a rough guess for the right end-point of the line search

    x1

    the left (smallest) anchor point for the search (usually 0)

    Definition Classes
    GoldenSectionLS → LineSearch
  3. def printGolden(): Unit

    Print the golden ratio and the golden section.

  4. def search(step: Double = 2.0): Double

    Perform an exact Line Search (LS) using the Golden Search Algorithm with defaults.

    Perform an exact Line Search (LS) using the Golden Search Algorithm with defaults.

    step

    the initial step size

    Definition Classes
    GoldenSectionLS → LineSearch