optimize._trustregion_dogleg

Dog-leg trust-region optimization.

Module Contents

Classes

DoglegSubproblem() Quadratic subproblem solved by the dogleg method

Functions

_minimize_dogleg(fun,x0,args=tuple,jac=None,hess=None,**trust_region_options) Minimization of scalar function of one or more variables using
_minimize_dogleg(fun, x0, args=tuple, jac=None, hess=None, **trust_region_options)

Minimization of scalar function of one or more variables using the dog-leg trust-region algorithm.

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.
class DoglegSubproblem

Quadratic subproblem solved by the dogleg method

cauchy_point()

The Cauchy point is minimal along the direction of steepest descent.

newton_point()

The Newton point is a global minimum of the approximate function.

solve(trust_radius)

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.

trust_radius : float
We are allowed to wander only this far away from the origin.
p : ndarray
The proposed step.
hits_boundary : bool
True if the proposed step is on the boundary of the trust region.

The Hessian is required to be positive definite.

[1]Jorge Nocedal and Stephen Wright, Numerical Optimization, second edition, Springer-Verlag, 2006, page 73.