newton | R Documentation |
Generalized newton optimizer used for the inner optimization problem.
newton(
par,
fn,
gr,
he,
trace = 1,
maxit = 100,
tol = 1e-08,
alpha = 1,
smartsearch = TRUE,
mgcmax = 1e+60,
super = TRUE,
silent = TRUE,
ustep = 1,
power = 0.5,
u0 = 1e-04,
grad.tol = tol,
step.tol = tol,
tol10 = 0.001,
env = environment(),
...
)
par |
Initial parameter. |
fn |
Objective function. |
gr |
Gradient function. |
he |
Sparse hessian function. |
trace |
Print tracing information? |
maxit |
Maximum number of iterations. |
tol |
Convergence tolerance. |
alpha |
Newton stepsize in the fixed stepsize case. |
smartsearch |
Turn on adaptive stepsize algorithm for non-convex problems? |
mgcmax |
Refuse to optimize if the maximum gradient component is too steep. |
super |
Supernodal Cholesky? |
silent |
Be silent? |
ustep |
Adaptive stepsize initial guess between 0 and 1. |
power |
Parameter controlling adaptive stepsize. |
u0 |
Parameter controlling adaptive stepsize. |
grad.tol |
Gradient convergence tolerance. |
step.tol |
Stepsize convergence tolerance. |
tol10 |
Try to exit if last 10 iterations not improved more than this. |
env |
Environment for cached Cholesky factor. |
... |
Currently unused. |
If smartsearch=FALSE
this function performs an ordinary newton optimization
on the function fn
using an exact sparse hessian function.
A fixed stepsize may be controlled by alpha
so that the iterations are
given by:
u_{n+1} = u_n - \alpha f''(u_n)^{-1}f'(u_n)
If smartsearch=TRUE
the hessian is allowed to become negative definite
preventing ordinary newton iterations. In this situation the newton iterations are performed on
a modified objective function defined by adding a quadratic penalty around the expansion point u_0
:
f_{t}(u) = f(u) + \frac{t}{2} \|u-u_0\|^2
This function's hessian ( f''(u)+t I
) is positive definite for t
sufficiently
large. The value t
is updated at every iteration: If the hessian is positive definite t
is
decreased, otherwise increased. Detailed control of the update process can be obtained with the
arguments ustep
, power
and u0
.
List with solution similar to optim
output.
newtonOption
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