{'fraction_non_alphanumeric': 0.015552099533437015, 'fraction_numerical': 0.003110419906687403, 'mean_word_length': 5.44, '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 recursive formulation of limited memory variable metric methods

: In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach enables to approximate of both the Hessian matrix and its inverse and can be used for an arbitrary update from the Broyden class (and some other updates). The new recursive formulation requires approximately 4 mn multiplications and additions for the direction determination, so it is comparable with other eﬃcient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, conﬁrm its practical eﬃciency.