{'fraction_non_alphanumeric': 0.013605442176870748, 'fraction_numerical': 0.0, 'mean_word_length': 5.445255474452555, '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}}
Mutual Impact of Numerical Linear Algebra and Large-Scale Optimization

The solution of linear systems for computing search directions is ubiquitous in optimization algorithms, being often the most computationally expensive task. Thus, effective numerical linear algebra is crucial for effective numerical optimization. Many optimization codes have benefited, in terms of both efficiency and robustness, from advances in numerical linear algebra algorithms and software. On the other hand, much progress in numerical linear algebra has been spurred by the need of solving linear systems with special features in the context of optimization. This talk addresses some critical aspects of this mutual impact. The focus is on the large and sparse case and considerable attention is given to the use of iterative approaches for solving linear systems within the interior point framework.