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__

Same as line_search_wolfe1, but fall back to line_search_wolfe2 if suitable step length is not found, and raise an exception if a suitable step length is not found.

Parameters:

• f (function) - function on which to perform the line search
• fprime (function) - gradient of the function on which to perform the line search
• xk (numpy.array) - point at which to start the search
• pk (numpy.array) - search direction
• gfk (numpy.array or None) - gradient of function evaluated at xk, if None is computed
• old_fval (float or None) - function evaluated at xk, if None is computed
• old_old_fval (float or None) - function evaluated at the point preceeding xk, or None if there isn't one

Returns: tuple

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