Class BFGS

Create an instance.

Parameters:

• c1 (float) - parameter for Armijo condition rule
• c2 (float) - parameter for curvature condition rule
• amax (float) - maximum allowable step size
• amin (float) - minimum allowable step size
• xtol (float) - nonnegative relative tolerance for an acceptable step, the search exits with a warning if the relative difference between sty and stx is less than xtol where sty and stx define an interval
• max_force (float) - maximum allowable force element
• max_iterations (int) - the maximum number of iterations
• eps (float) - step size in Angstrom for any finite difference approximations
• init_hess (str) - the type of initial Hessian to use
• verbose (bool) - specifies verbose logging
• logger (logging.Logger or None) - output logger or None if there isn't one

Overrides: object.__init__

As `scalar_search_wolfe1` but do a line search to direction `pk`

Parameters
----------
f : callable
    Function `f(x)`
fprime : callable
    Gradient of `f`
xk : array_like
    Current point
pk : array_like
    Search direction

gfk : array_like, optional
    Gradient of `f` at point `xk`
old_fval : float, optional
    Value of `f` at point `xk`
old_old_fval : float, optional
    Value of `f` at point preceding `xk`

The rest of the parameters are the same as for `scalar_search_wolfe1`.

Returns
-------
stp, f_count, g_count, fval, old_fval
    As in `line_search_wolfe1`
gval : array
    Gradient of `f` at the final point

Scalar function search for alpha that satisfies strong Wolfe conditions

alpha > 0 is assumed to be a descent direction.

Parameters
----------
phi : callable phi(alpha)
    Function at point `alpha`
derphi : callable dphi(alpha)
    Derivative `d phi(alpha)/ds`. Returns a scalar.

phi0 : float, optional
    Value of `f` at 0
old_phi0 : float, optional
    Value of `f` at the previous point
derphi0 : float, optional
    Value `derphi` at 0
amax : float, optional
    Maximum step size
c1, c2 : float, optional
    Wolfe parameters

Returns
-------
alpha : float
    Step size, or None if no suitable step was found
phi : float
    Value of `phi` at the new point `alpha`
phi0 : float
    Value of `phi` at `alpha=0`

Notes
-----
Uses routine DCSRCH from MINPACK.

Return an initial guess for the inverse Hessian.

Parameters:

• fun (function) - function to minimize
• jac (function) - the Jacobian of the function being minimized
• fun_0 (float) - function value at initial solution
• jac_0 (float) - the Jacobian value at initial solution
• x_0 (numpy.array) - initial solution

Returns: numpy.array

the initial guess inverse Hessian (N/3 X 3)

Minimization of a function using the BFGS algorithm.

Parameters:

• fun (function) - function to minimize
• x_0 (numpy.array) - initial solution
• jac (function) - the Jacobian of the function being minimized

Returns: scipy.optimize.optimize.OptimizeResult

optimization parameters