2.1. copt.minimize_TOS

copt.minimize_TOS(f_grad, x0, prox_1=None, prox_2=None, tol=1e-06, max_iter=1000, verbose=0, callback=None, backtracking=True, step_size=None, max_iter_backtracking=100, backtracking_factor=0.7, h_Lipschitz=None)[source]

Davis-Yin three operator splitting method.

This algorithm can solve problems of the form

minimize_x f(x) + g(x) + h(x)

where f is a smooth function and g is a (possibly non-smooth) function for which the proximal operator is known.

Parameters:
  • f_grad (callable) – Returns the function value and gradient of the objective function. With return_gradient=False, returns only the function value.
  • prox_1 (callable or None) – prox_1(x, alpha, *args) returns the proximal operator of g at xa with parameter alpha. Extra arguments can be passed by prox_1_args.
  • y0 (array-like) – Initial guess
  • backtracking (boolean) – Whether to perform backtracking (i.e. line-search) to estimate the step size.
  • max_iter (int) – Maximum number of iterations.
  • verbose (int) – Verbosity level, from 0 (no output) to 2 (output on each iteration)
  • step_size (float) – Starting value for the line-search procedure.
  • callback (callable) – callback function (optional).
Returns:

res – The optimization result represented as a scipy.optimize.OptimizeResult object. Important attributes are: x the solution array, success a Boolean flag indicating if the optimizer exited successfully and message which describes the cause of the termination. See scipy.optimize.OptimizeResult for a description of other attributes.

Return type:

OptimizeResult

References