3.2.5. horton.correlatedwfn.trustregionopt – Optimization of Newton step¶
Module contains different trust radius optimization algorithms
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class
horton.correlatedwfn.trustregionopt.Dogleg(pn, g, H, radius)¶ Powell’s single dogleg steps approximate the trust region step over the two dimensional subspace spanned by the Cauchy step and any Newton step. Depending on the size of current step length, the step is adjusted yielding one of the following steps:
- if p(newton) < radius: Do full Newton step (not calculated here)
- elif p(cauchy) > radius: Do Cauchy step
- else: Do dogleg step
** Arguements **
- pn
- The full Newton step
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
- radius
- The current trustradius
** Returns **
step: final step, a OneIndex instance stepNorm: Euclidian norm of the step -
__call__()¶ The dogleg algorithm.
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__init__(pn, g, H, radius)¶ Powell’s single dogleg steps approximate the trust region step over the two dimensional subspace spanned by the Cauchy step and any Newton step. Depending on the size of current step length, the step is adjusted yielding one of the following steps:
- if p(newton) < radius: Do full Newton step (not calculated here)
- elif p(cauchy) > radius: Do Cauchy step
- else: Do dogleg step
** Arguements **
- pn
- The full Newton step
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
- radius
- The current trustradius
** Returns **
step: final step, a OneIndex instance stepNorm: Euclidian norm of the step
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class
horton.correlatedwfn.trustregionopt.DoubleDogleg(pn, g, H, radius)¶ Double dogleg steps approximate the trust region step
- if ||p(g)|| >= radius: Do step in g direction
- elif c*||p(n)|| >= radius: Do ddl step
- elif ||p(n)|| >= radius: Do scaled Newton step
- else: Do Newton step
** Arguements **
- pn
- The full Newton step
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
- radius
- The current trustradius
** Returns **
step: final step, a OneIndex instance stepNorm: Euclidian norm of the step -
__call__()¶ The double dogleg algorithm.
-
__init__(pn, g, H, radius)¶ Double dogleg steps approximate the trust region step
- if ||p(g)|| >= radius: Do step in g direction
- elif c*||p(n)|| >= radius: Do ddl step
- elif ||p(n)|| >= radius: Do scaled Newton step
- else: Do Newton step
** Arguements **
- pn
- The full Newton step
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
- radius
- The current trustradius
** Returns **
step: final step, a OneIndex instance stepNorm: Euclidian norm of the step
-
class
horton.correlatedwfn.trustregionopt.TruncatedCG(lf, g, H, radius, **kwargs)¶ Solve the quadratic trust-region subproblem
minimize < g, s > + 1/2 < s, Hs > subject to < s, s > <= radiusby means of the truncated conjugate gradient algorithm as described in Trond Steihaug, SIAM Journal on Numerical Analysis (1983), 20, 626-637.
The algorithm stops as soon as the preconditioned norm of the gradient falls under
max( abstol, reltol * g0 )where g0 is the preconditioned norm of the initial gradient (or the Euclidian norm if no preconditioner is given), or as soon as the iterates cross the boundary of the trust region.
** Arguements **
- lf
- A linalg factory instance
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
** Returns **
step: final step niter: number of iterations stepNorm: Euclidian norm of the step -
__call__(**kwargs)¶ Solve the trust-region subproblem.
** Keywords **
s0: initial guess (default: [0,0,…,0]), abstol: absolute stopping tolerance (default: 1.0e-8), reltol: relative stopping tolerance (default: 1.0e-6), maxiter: maximum number of iterations (default: 2n), prec: a user-defined preconditioner.
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__init__(lf, g, H, radius, **kwargs)¶ Solve the quadratic trust-region subproblem
minimize < g, s > + 1/2 < s, Hs > subject to < s, s > <= radiusby means of the truncated conjugate gradient algorithm as described in Trond Steihaug, SIAM Journal on Numerical Analysis (1983), 20, 626-637.
The algorithm stops as soon as the preconditioned norm of the gradient falls under
max( abstol, reltol * g0 )where g0 is the preconditioned norm of the initial gradient (or the Euclidian norm if no preconditioner is given), or as soon as the iterates cross the boundary of the trust region.
** Arguements **
- lf
- A linalg factory instance
- g
- The gradient, a OneIndex instance
- H
- The Hessian, a OneIndex instance
** Returns **
step: final step niter: number of iterations stepNorm: Euclidian norm of the step
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to_boundary(s, p, radius, ss=None)¶ Given vectors s and p and a trust-region radius radius > 0, return the positive scalar sigma such that
|| s + sigma * p || = radiusin Euclidian norm. If known, supply optional argument ss whose value should be the squared Euclidian norm of s.