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83 lines
2.6 KiB
Go
83 lines
2.6 KiB
Go
// Copyright ©2014 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package optimize
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const (
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defaultBacktrackingContraction = 0.5
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defaultBacktrackingDecrease = 1e-4
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minimumBacktrackingStepSize = 1e-20
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)
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// Backtracking is a Linesearcher that uses backtracking to find a point that
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// satisfies the Armijo condition with the given decrease factor. If the Armijo
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// condition has not been met, the step size is decreased by ContractionFactor.
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//
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// The Armijo condition only requires the gradient at the beginning of each
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// major iteration (not at successive step locations), and so Backtracking may
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// be a good linesearch for functions with expensive gradients. Backtracking is
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// not appropriate for optimizers that require the Wolfe conditions to be met,
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// such as BFGS.
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//
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// Both DecreaseFactor and ContractionFactor must be between zero and one, and
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// Backtracking will panic otherwise. If either DecreaseFactor or
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// ContractionFactor are zero, it will be set to a reasonable default.
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type Backtracking struct {
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DecreaseFactor float64 // Constant factor in the sufficient decrease (Armijo) condition.
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ContractionFactor float64 // Step size multiplier at each iteration (step *= ContractionFactor).
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stepSize float64
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initF float64
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initG float64
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lastOp Operation
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}
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func (b *Backtracking) Init(f, g float64, step float64) Operation {
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if step <= 0 {
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panic("backtracking: bad step size")
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}
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if g >= 0 {
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panic("backtracking: initial derivative is non-negative")
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}
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if b.ContractionFactor == 0 {
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b.ContractionFactor = defaultBacktrackingContraction
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}
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if b.DecreaseFactor == 0 {
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b.DecreaseFactor = defaultBacktrackingDecrease
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}
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if b.ContractionFactor <= 0 || b.ContractionFactor >= 1 {
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panic("backtracking: ContractionFactor must be between 0 and 1")
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}
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if b.DecreaseFactor <= 0 || b.DecreaseFactor >= 1 {
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panic("backtracking: DecreaseFactor must be between 0 and 1")
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}
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b.stepSize = step
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b.initF = f
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b.initG = g
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b.lastOp = FuncEvaluation
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return b.lastOp
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}
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func (b *Backtracking) Iterate(f, _ float64) (Operation, float64, error) {
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if b.lastOp != FuncEvaluation {
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panic("backtracking: Init has not been called")
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}
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if ArmijoConditionMet(f, b.initF, b.initG, b.stepSize, b.DecreaseFactor) {
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b.lastOp = MajorIteration
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return b.lastOp, b.stepSize, nil
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}
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b.stepSize *= b.ContractionFactor
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if b.stepSize < minimumBacktrackingStepSize {
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b.lastOp = NoOperation
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return b.lastOp, b.stepSize, ErrLinesearcherFailure
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}
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b.lastOp = FuncEvaluation
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return b.lastOp, b.stepSize, nil
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}
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