forte2.helpers.lbfgs

Module Contents

class forte2.helpers.lbfgs.LBFGS

Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer.

Parameters:

mint, optional, default=6

The number of vectors to keep in memory for the L-BFGS update.

epsilonfloat, optional, default=1.0e-5

Convergence threshold to terminate the minimization: |g| < ε * max(1, |x|).

maxiterint, optional, default=20

Maximum number of iterations for the optimization.

maxiter_linesearchint, optional, default=5

Maximum number of trials for line search to find the optimal step length.

max_dirfloat, optional, default=1.0e15

Maximum absolute value allowed in the direction vector.

line_search_conditionstr, optional, default=’strong_wolfe’

Condition to terminate line search backtracking. Options are ‘armijo’, ‘wolfe’, or ‘strong_wolfe’.

step_length_methodstr, optional, default=’line_bracketing_zoom’

Method to determine step lengths. Options are ‘max_correction’, ‘line_backtracking’, or ‘line_bracketing_zoom’.

min_stepfloat, optional, default=1.0e-15

Minimum step length allowed during line search.

max_stepfloat, optional, default=1.0e15

Maximum step length allowed during line search.

c1float, optional, default=1.0e-4

Parameter for the Armijo condition in line search.

c2float, optional, default=0.9

Parameter for the Wolfe curvature condition in line search.

Notes

Translated into Python from Forte v1: evangelistalab/forte For implementation details, see Wikipedia https://en.wikipedia.org/wiki/Limited-memory_BFGS and Numerical Optimization 2nd Ed. by Jorge Nocedal and Stephen J. Wright

m: int = 6

epsilon: float = 1e-05

maxiter: int = 20

maxiter_linesearch: int = 5

max_dir: float = 1000000000000000.0

line_search_condition: str = 'strong_wolfe'

step_length_method: str = 'line_bracketing_zoom'

min_step: float = 1e-15

max_step: float = 1000000000000000.0

c1: float = 0.0001

c2: float = 0.9

log_level: int

warn_if_not_converged: bool = False

dtype: type

converged: bool = False

iter: int = 0

p: numpy.typing.NDArray

minimize(obj, x)

The minimization for the objective function

Parameters:

objobject

Target function to minimize, it should should be encapsulated in a class that has the following methods: fx, g = obj.evaluate(x, g, do_g=True) where gradient g is modified by the function, fx is the function return value, and g is computed when do_g==True. If diagonal Hessian is specified, h0 = obj.hess_diag(x) should be available.

xNDArray

The initial value of x as input, the final value of x as output.

Returns:

fxfloat

The function value at optimized x.

class forte2.helpers.lbfgs.LBFGS_scipy

A wrapper for the SciPy L-BFGS optimization. For debug use only.

epsilon: float = 1e-05

maxiter: int = 20

c1: float = 0.0001

c2: float = 0.9

print: int = 1

m: int = 6

maxiter_linesearch: int = 5

max_dir: float = 1000000000000000.0

line_search_condition: str = 'strong_wolfe'

step_length_method: str = 'line_bracketing_zoom'

min_step: float = 1e-15

max_step: float = 1000000000000000.0

minimize(obj, x)

class forte2.helpers.lbfgs.NewtonRaphson

epsilon: float = 1e-05

maxiter: int = 20

c1: float = 0.0001

c2: float = 0.9

print: int = 1

m: int = 6

maxiter_linesearch: int = 5

max_dir: float = 1000000000000000.0

line_search_condition: str = 'strong_wolfe'

step_length_method: str = 'line_bracketing_zoom'

min_step: float = 1e-15

max_step: float = 1000000000000000.0

minimize(obj, x)