desc.optimize.fmintr

class desc.optimize.fmintr(fun, x0, grad, hess='bfgs', args=(), method='dogleg', x_scale=1, ftol=1e-06, xtol=1e-06, gtol=1e-06, verbose=1, maxiter=None, callback=None, options={})[source]

Minimize a scalar function using a (quasi)-Newton trust region method.

Parameters:

  • fun (callable) – objective to be minimized. Should have a signature like fun(x,*args)-> float

  • x0 (array-like) – initial guess

  • grad (callable) – function to compute gradient, df/dx. Should take the same arguments as fun

  • hess (callable or 'bfgs', optional:) – function to compute Hessian matrix of fun, or 'bfgs' in which case the BFGS method will be used to approximate the Hessian.

  • args (tuple) – additional arguments passed to fun, grad, and hess

  • method ('dogleg' or 'subspace') – method to use for trust region subproblem

  • x_scale (array_like or 'hess', optional) – Characteristic scale of each variable. Setting x_scale is equivalent to reformulating the problem in scaled variables xs = x / x_scale. An alternative view is that the size of a trust region along jth dimension is proportional to x_scale[j]. Improved convergence may be achieved by setting x_scale such that a step of a given size along any of the scaled variables has a similar effect on the cost function. If set to 'hess', the scale is iteratively updated using the inverse norms of the columns of the Hessian matrix.

  • ftol (float or None, optional) – Tolerance for termination by the change of the cost function. Default is 1e-8. The optimization process is stopped when dF < ftol * F, and there was an adequate agreement between a local quadratic model and the true model in the last step. If None, the termination by this condition is disabled.

  • xtol (float or None, optional) – Tolerance for termination by the change of the independent variables. Default is 1e-8. Optimization is stopped when norm(dx) < xtol * (xtol + norm(x)). If None, the termination by this condition is disabled.

  • gtol (float or None, optional) – Absolute tolerance for termination by the norm of the gradient. Default is 1e-8. Optimizer teriminates when norm(g) < gtol, where If None, the termination by this condition is disabled.

  • verbose ({0, 1, 2}, optional) –

    • 0 (default) : work silently.

    • 1 : display a termination report.

    • 2 : display progress during iterations

  • maxiter (int, optional) – maximum number of iterations. Defaults to size(x)*100

  • callback (callable, optional) –

    Called after each iteration. Should be a callable with the signature:

    callback(xk, OptimizeResult state) -> bool

    where xk is the current parameter vector. and state is an OptimizeResult object, with the same fields as the ones from the return. If callback returns True the algorithm execution is terminated.

  • options (dict, optional) – dictionary of optional keyword arguments to override default solver settings. See the code for more details.

Returns:

res (OptimizeResult) – The optimization result represented as a OptimizeResult object. Important attributes are: x the solution array, success a Boolean flag indicating if the optimizer exited successfully.