scalation.optimization.WolfeLS3
The WolfeLS3 class performs an inexact line search on f to find (1) a point x that exhibits (1) SDC: sufficient decrease (f(x) enough less that f(0)) and (2) CC: the slope at x is less steep than the slope at 0. That is, the line search looks for a value for x satisfying the two Wolfe conditions.
f(x) <= f(0) + c1 * f'(0) * x Wolfe condition 1 (Armijo condition) |f'(x)| <= |c2 * f'(0)| Wolfe condition 2 (Strong version) f'(x) >= c2 * f'(0) Wolfe condition 2 (Weak version, more robust)
The it uses bisection (or interpolative search) to find an approximate local minimal point. Currently, the strong version is not supported. Note: c1 and c2 defaults below intended for Quasi Newton methods such as BFGS or L-BFGS
Value parameters
c1
constant for sufficient decrease (Wolfe condition 1: .0001 to .001)
c2
constant for curvature/slope constraint (Wolfe condition 2: .9 to .8)
c3
constant for noise control condition
eg
estimate of gradient noise
f
the objective/loss function to minimize
g
the gradient of the objective/loss function
Attributes
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Supertypes
class Object
trait Matchable
class Any
Members list
Two-Phase Armijo-Wolfe Line Search and Lengthening: Initial Phase, Algorithm 3.2 in
Two-Phase Armijo-Wolfe Line Search and Lengthening: Initial Phase, Algorithm 3.2 in
Value parameters
p
the current search direction
step
the initial step size
x
the current point
Attributes
See also
arch.library.northwestern.edu/concern/generic_works/jm214p59n?locale=en
Return whether the noise control condition is satisfied.
Return whether the noise control condition is satisfied.
Value parameters
gx
the gradient at original point x
gy
the gradient at new point y = x + p * a
p
the search direction
Attributes
Two-Phase Armijo-Wolfe Line Search and Lengthening: Split Phase, Algorithm 3.3 in
Two-Phase Armijo-Wolfe Line Search and Lengthening: Split Phase, Algorithm 3.3 in
Value parameters
a_
the initial step length
b_
the initial lengthening parameter
fx
the functional value at x
gx
the gradient at x
gxp
the dot product if g(x) and p
p
the search direction
x
the initial point
Attributes
See also
arch.library.northwestern.edu/concern/generic_works/jm214p59n?locale=en
Return whether Wolfe condition 1, the Sufficient Decrease Condition (SDC) is satisfied.
Return whether Wolfe condition 1, the Sufficient Decrease Condition (SDC) is satisfied.
Value parameters
a
the displacement in the search direction
fx
the functional value of the original point
fy
the functional value of the new point y = x + p * a
gxp
the dot product of the gradient vector g(x) and the search vector p
Attributes
Return whether Wolfe condition 2, the Curvature Condition (CC) is satisfied.
Return whether Wolfe condition 2, the Curvature Condition (CC) is satisfied.
Value parameters
gxp
the dot product of the gradient vector g(x) and the search vector p
gy
the gradient at new point y = x + p * a
p
the search direction vector
Attributes