copt.minimize_TOS¶

copt.
minimize_TOS
(f_grad, x0, g_prox=None, h_prox=None, tol=1e06, max_iter=1000, verbose=0, callback=None, line_search=True, step_size=None, max_iter_backtracking=100, backtracking_factor=0.7, h_Lipschitz=None)[source]¶ DavisYin 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 nonsmooth) 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 (arraylike) – Initial guess
 line_search (boolean) – Whether to perform backtracking (i.e. linesearch) 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 linesearch 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 andmessage
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 threeoperator splitting scheme and its optimization applications.” arXiv preprint arXiv:1504.01032 (2015) https://arxiv.org/abs/1504.01032