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Minimization of scalar function of one or more variables using
the dog-leg trust-region algorithm.
Options
-------
initial_trust_radius : float
Initial trust-region radius.
max_trust_radius : float
Maximum value of the trust-region radius. No steps that are longer
than this value will be proposed.
eta : float
Trust region related acceptance stringency for proposed steps.
gtol : float
Gradient norm must be less than `gtol` before successful
termination.
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Minimize a function using the dog-leg trust-region algorithm.
This algorithm requires function values and first and second derivatives.
It also performs a costly Hessian decomposition for most iterations,
and the Hessian is required to be positive definite.
Parameters
----------
trust_radius : float
We are allowed to wander only this far away from the origin.
Returns
-------
p : ndarray
The proposed step.
hits_boundary : bool
True if the proposed step is on the boundary of the trust region.
Notes
-----
The Hessian is required to be positive definite.
References
----------
.. [1] Jorge Nocedal and Stephen Wright,
Numerical Optimization, second edition,
Springer-Verlag, 2006, page 73.
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