class GradientDescent extends Minimizer with Error
The GradientDescent class solves unconstrained Non-Linear Programming (NLP)
problems using the Gradient Descent algorithm. Given a function 'f' and a
starting point 'x0', the algorithm computes the gradient and takes steps in
the opposite direction. The algorithm iterates until it converges. The class
assumes that partial derivative functions are not available unless explicitly
given via the 'setDerivatives' method.
dir_k = -gradient (x)
minimize f(x)
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new
GradientDescent(f: FunctionV2S, exactLS: Boolean = true)
- f
the vector-to-scalar objective function
- exactLS
whether to use exact (e.g.,
GoldenLS) or inexact (e.g.,WolfeLS) Line Search
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val
EPSILON: Double
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val
MAX_ITER: Int
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val
STEP: Double
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val
TOL: Double
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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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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.
- x
the current point
- dir
the direction to move in
- step
the initial step size
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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
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def
solve(x0: VectorD, step: Double = STEP, toler: Double = EPSILON): VectorD
Solve the Non-Linear Programming (NLP) problem using the Gradient Descent algorithm.
Solve the Non-Linear Programming (NLP) problem using the Gradient Descent algorithm.
- x0
the starting point
- step
the initial step size
- toler
the tolerance
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