copt.fmin_DavisYin

copt.fmin_DavisYin(fun, fun_deriv, g_prox, h_prox, y0, alpha=1.0, beta=1.0, tol=1e-06, max_iter=1000, g_prox_args=(), h_prox_args=(), verbose=0, callback=None, backtracking=True, step_size=None, max_iter_backtracking=100, backtracking_factor=0.4)[source]

Davis-Yin three operator splitting method.

This algorithm can solve problems of the form

minimize_x f(x) + alpha * g(x) + beta * h(x)

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

Parameters:
  • fun (callable) – f(x) returns the value of f at x.
  • fun_deriv (callable or None) – f_prime(x) returns the gradient of f.
  • g_prox (callable or None) – g_prox(x, alpha, *args) returns the proximal operator of g at xa with parameter alpha. Extra arguments can be passed by g_prox_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

Davis, Damek, and Wotao Yin. “A three-operator splitting scheme and its optimization applications.” arXiv preprint arXiv:1504.01032 (2015) https://arxiv.org/abs/1504.01032

Pedregosa, Fabian. “On the convergence rate of the three operator splitting scheme.” arXiv preprint arXiv:1610.07830 (2016) https://arxiv.org/abs/1610.07830