copt.minimize_vrtos

copt.minimize_vrtos(f_deriv, A, b, x0, step_size, prox_1=None, prox_2=None, alpha=0, max_iter=500, tol=1e-06, callback=None, verbose=0)

Variance-reduced three operator splitting (VRTOS) algorithm.

The VRTOS algorithm can solve optimization problems of the form

argmin_{x in R^p} sum_{i}^n_samples f(A_i^T x, b_i) + alpha * ||x||_2^2 +

• pen1(x) + pen2(x)

Parameters

• f_deriv – derivative of f

• x0 (np.ndarray or None, optional) – Starting point for optimization.

• step_size (float or None, optional) – Step size for the optimization. If None is given, this will be estimated from the function f.

• n_jobs (int) – Number of threads to use in the optimization. A number higher than 1 will use the Asynchronous SAGA optimization method described in [Pedregosa et al., 2017]

• max_iter (int) – Maximum number of passes through the data in the optimization.

• tol (float) – Tolerance criterion. The algorithm will stop whenever the norm of the gradient mapping (generalization of the gradient for nonsmooth optimization) is below tol.

• verbose (bool) – Verbosity level. True might print some messages.

• trace (bool) – Whether to trace convergence of the function, useful for plotting and/or debugging. If ye, the result will have extra members trace_func, trace_time.

Returns

opt – 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

Pedregosa, Fabian, Kilian Fatras, and Mattia Casotto. “Variance Reduced Three Operator Splitting.” arXiv preprint arXiv:1806.07294 (2018).