{'fraction_non_alphanumeric': 0.015306122448979591, 'fraction_numerical': 0.0, 'mean_word_length': 5.583892617449664, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A second order primal-dual algorithm for nonsmooth convex composite optimization

We develop a second order primal-dual algorithm for nonsmooth convex composite optimization problems in which the objective function is given by the sum of a twice dif-ferentiable term and a possibly non-differentiable regularizer. After introducing an auxiliary variable, we utilize the proximal operator of the nonsmooth regularizer to transform the associated augmented Lagrangian into a continuously differentiable function, the proximal augmented Lagrangian. We employ a generalization of the Jacobian to define second order updates on this function which locally converge quadratically/superlinearly to the optimal solution. We then use a merit function to develop a customized algorithm in which the search direction can be computed efficiently for large values of the regularization parameter. Finally, we illustrate the utility of our method using the l\-regularized least squares problem.