Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2963086517', 'doi': 'https://doi.org/10.1609/aaai.v32i1.11802', 'title': 'Inexact Proximal Gradient Methods for Non-Convex and Non-Smooth Optimization', 'display_name': 'Inexact Proximal Gradient Methods for Non-Convex and Non-Smooth Optimization', 'publication_year': 2018, 'publication_date': '2018-04-29', 'ids': {'openalex': 'https://openalex.org/W2963086517', 'doi': 'https://doi.org/10.1609/aaai.v32i1.11802', 'mag': '2963086517'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1609/aaai.v32i1.11802', 'pdf_url': 'https://ojs.aaai.org/index.php/AAAI/article/download/11802/11661', 'source': {'id': 'https://openalex.org/S4210191458', 'display_name': 'Proceedings of the AAAI Conference on Artificial Intelligence', 'issn_l': '2159-5399', 'issn': ['2159-5399', '2374-3468'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310320058', 'host_organization_name': 'Association for the Advancement of Artificial Intelligence', 'host_organization_lineage': ['https://openalex.org/P4310320058'], 'host_organization_lineage_names': ['Association for the Advancement of Artificial Intelligence'], 'type': 'conference'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://ojs.aaai.org/index.php/AAAI/article/download/11802/11661', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5069728539', 'display_name': 'Bin Gu', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I170201317', 'display_name': 'University of Pittsburgh', 'ror': 'https://ror.org/01an3r305', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I170201317']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Bin Gu', 'raw_affiliation_strings': ['University of Pittsburgh'], 'affiliations': [{'raw_affiliation_string': 'University of Pittsburgh', 'institution_ids': ['https://openalex.org/I170201317']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5101851754', 'display_name': 'Wang De', 'orcid': 'https://orcid.org/0000-0002-4218-4448'}, 'institutions': [{'id': 'https://openalex.org/I189196454', 'display_name': 'The University of Texas at Arlington', 'ror': 'https://ror.org/019kgqr73', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I189196454']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'De Wang', 'raw_affiliation_strings': ['University of Texas at Arlington'], 'affiliations': [{'raw_affiliation_string': 'University of Texas at Arlington', 'institution_ids': ['https://openalex.org/I189196454']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5069872293', 'display_name': 'Zhouyuan Huo', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I170201317', 'display_name': 'University of Pittsburgh', 'ror': 'https://ror.org/01an3r305', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I170201317']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Zhouyuan Huo', 'raw_affiliation_strings': ['University of Pittsburgh'], 'affiliations': [{'raw_affiliation_string': 'University of Pittsburgh', 'institution_ids': ['https://openalex.org/I170201317']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5060016795', 'display_name': 'Heng Huang', 'orcid': 'https://orcid.org/0000-0002-3483-8333'}, 'institutions': [{'id': 'https://openalex.org/I170201317', 'display_name': 'University of Pittsburgh', 'ror': 'https://ror.org/01an3r305', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I170201317']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Heng Huang', 'raw_affiliation_strings': ['University of Pittsburgh'], 'affiliations': [{'raw_affiliation_string': 'University of Pittsburgh', 'institution_ids': ['https://openalex.org/I170201317']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 3.482, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 24, 'citation_normalized_percentile': {'value': 0.999428, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 92, 'max': 93}, 'biblio': {'volume': '32', 'issue': '1', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10500', 'display_name': 'Sparse and Compressive Sensing Techniques', 'score': 0.9976, 'subfield': {'id': 'https://openalex.org/subfields/2206', 'display_name': 'Computational Mechanics'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10500', 'display_name': 'Sparse and Compressive Sensing Techniques', 'score': 0.9976, 'subfield': {'id': 'https://openalex.org/subfields/2206', 'display_name': 'Computational Mechanics'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11612', 'display_name': 'Stochastic Gradient Optimization Techniques', 'score': 0.9878, 'subfield': {'id': 'https://openalex.org/subfields/1702', 'display_name': 'Artificial Intelligence'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10545', 'display_name': 'Optimization and Variational Analysis', 'score': 0.9217, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/proximal-gradient-methods', 'display_name': 'Proximal Gradient Methods', 'score': 0.9707346}, {'id': 'https://openalex.org/keywords/regularization', 'display_name': 'Regularization', 'score': 0.5032689}, {'id': 'https://openalex.org/keywords/operator', 'display_name': 'Operator (biology)', 'score': 0.47096995}], 'concepts': [{'id': 'https://openalex.org/C10494615', 'wikidata': 'https://www.wikidata.org/wiki/Q17086765', 'display_name': 'Proximal Gradient Methods', 'level': 4, 'score': 0.9707346}, {'id': 'https://openalex.org/C79248915', 'wikidata': 'https://www.wikidata.org/wiki/Q17086776', 'display_name': 'Proximal gradient methods for learning', 'level': 5, 'score': 0.76414543}, {'id': 'https://openalex.org/C115680565', 'wikidata': 'https://www.wikidata.org/wiki/Q5977448', 'display_name': 'Gradient method', 'level': 2, 'score': 0.5964627}, {'id': 'https://openalex.org/C112680207', 'wikidata': 'https://www.wikidata.org/wiki/Q714886', 'display_name': 'Regular polygon', 'level': 2, 'score': 0.56362826}, {'id': 'https://openalex.org/C157972887', 'wikidata': 'https://www.wikidata.org/wiki/Q463359', 'display_name': 'Convex optimization', 'level': 3, 'score': 0.51780427}, {'id': 'https://openalex.org/C2776135515', 'wikidata': 'https://www.wikidata.org/wiki/Q17143721', 'display_name': 'Regularization (linguistics)', 'level': 2, 'score': 0.5032689}, {'id': 'https://openalex.org/C126255220', 'wikidata': 'https://www.wikidata.org/wiki/Q141495', 'display_name': 'Mathematical optimization', 'level': 1, 'score': 0.48725143}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.48655882}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.482231}, {'id': 'https://openalex.org/C145446738', 'wikidata': 'https://www.wikidata.org/wiki/Q319913', 'display_name': 'Convex function', 'level': 3, 'score': 0.47219527}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.4719994}, {'id': 'https://openalex.org/C2777303404', 'wikidata': 'https://www.wikidata.org/wiki/Q759757', 'display_name': 'Convergence (economics)', 'level': 2, 'score': 0.47189984}, {'id': 'https://openalex.org/C17020691', 'wikidata': 'https://www.wikidata.org/wiki/Q139677', 'display_name': 'Operator (biology)', 'level': 5, 'score': 0.47096995}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.38103086}, {'id': 'https://openalex.org/C111110010', 'wikidata': 'https://www.wikidata.org/wiki/Q2627315', 'display_name': 'Convex combination', 'level': 4, 'score': 0.27743936}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.21321204}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.058498025}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C158448853', 'wikidata': 'https://www.wikidata.org/wiki/Q425218', 'display_name': 'Repressor', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C86339819', 'wikidata': 'https://www.wikidata.org/wiki/Q407384', 'display_name': 'Transcription factor', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C50522688', 'wikidata': 'https://www.wikidata.org/wiki/Q189833', 'display_name': 'Economic growth', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1609/aaai.v32i1.11802', 'pdf_url': 'https://ojs.aaai.org/index.php/AAAI/article/download/11802/11661', 'source': {'id': 'https://openalex.org/S4210191458', 'display_name': 'Proceedings of the AAAI Conference on Artificial Intelligence', 'issn_l': '2159-5399', 'issn': ['2159-5399', '2374-3468'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310320058', 'host_organization_name': 'Association for the Advancement of Artificial Intelligence', 'host_organization_lineage': ['https://openalex.org/P4310320058'], 'host_organization_lineage_names': ['Association for the Advancement of Artificial Intelligence'], 'type': 'conference'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1612.06003', 'pdf_url': 'https://arxiv.org/pdf/1612.06003', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1609/aaai.v32i1.11802', 'pdf_url': 'https://ojs.aaai.org/index.php/AAAI/article/download/11802/11661', 'source': {'id': 'https://openalex.org/S4210191458', 'display_name': 'Proceedings of the AAAI Conference on Artificial Intelligence', 'issn_l': '2159-5399', 'issn': ['2159-5399', '2374-3468'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310320058', 'host_organization_name': 'Association for the Advancement of Artificial Intelligence', 'host_organization_lineage': ['https://openalex.org/P4310320058'], 'host_organization_lineage_names': ['Association for the Advancement of Artificial Intelligence'], 'type': 'conference'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 24, 'referenced_works': ['https://openalex.org/W1573301526', 'https://openalex.org/W1673797905', 'https://openalex.org/W1849979240', 'https://openalex.org/W1903303072', 'https://openalex.org/W1986534176', 'https://openalex.org/W1987083649', 'https://openalex.org/W2019786292', 'https://openalex.org/W2047152541', 'https://openalex.org/W2052725501', 'https://openalex.org/W2082074261', 'https://openalex.org/W2097417531', 'https://openalex.org/W2100556411', 'https://openalex.org/W2117756735', 'https://openalex.org/W2119200797', 'https://openalex.org/W2137823674', 'https://openalex.org/W2145831204', 'https://openalex.org/W2154202969', 'https://openalex.org/W2166956514', 'https://openalex.org/W2168914046', 'https://openalex.org/W2184634347', 'https://openalex.org/W2950952569', 'https://openalex.org/W3012264151', 'https://openalex.org/W4205213118', 'https://openalex.org/W4300807924'], 'related_works': ['https://openalex.org/W4292651679', 'https://openalex.org/W4287828482', 'https://openalex.org/W3208916810', 'https://openalex.org/W3009102021', 'https://openalex.org/W2970498479', 'https://openalex.org/W2963086517', 'https://openalex.org/W2570633406', 'https://openalex.org/W2564735875', 'https://openalex.org/W2034189051', 'https://openalex.org/W1543207628'], 'abstract_inverted_index': {'In': [0], 'machine': [1], 'learning': [2, 147], 'research,': [3], 'the': [4, 28, 34, 61, 83, 94, 98, 116, 121, 129, 135, 152], 'proximal': [5, 19, 29, 35, 46, 57, 79, 111, 125, 140, 158], 'gradient': [6, 20, 47, 58, 80, 112, 126, 141, 159], 'methods': [7, 21, 48, 59], 'are': [8, 22], 'popular': [9], 'for': [10], 'solving': [11, 27], 'various': [12], 'optimization': [13], 'problems': [14], 'with': [15], 'non-smooth': [16], 'regularization.': [17], 'Inexact': [18], 'extremely': [23], 'important': [24], 'when': [25], 'exactly': [26], 'operator': [30, 36], 'is': [31, 64], 'time-consuming,': [32], 'or': [33], 'does': [37], 'not': [38], 'have': [39, 115], 'an': [40], 'analytic': [41], 'solution.': [42], 'However,': [43], 'existing': [44], 'inexact': [45, 56, 78, 110, 139, 157], 'only': [49], 'consider': [50], 'convex': [51], 'problems.': [52, 148], 'The': [53, 104], 'knowledge': [54], 'of': [55, 123, 137, 154], 'in': [60, 71, 128], 'non-convex': [62, 130, 146], 'setting': [63], 'very': [65], 'limited.': [66], 'To': [67], 'address': [68], 'this': [69, 72], 'challenge,': [70], 'paper,': [73], 'we': [74, 92, 133], 'first': [75], 'propose': [76], 'three': [77, 144], 'algorithms,': [81], 'including': [82], 'basic': [84, 99], 'version': [85], 'and': [86, 100], 'Nesterov’s': [87, 101], 'accelerated': [88, 102], 'version.': [89], 'After': [90], 'that,': [91], 'provide': [93], 'theoretical': [95, 105], 'analysis': [96], 'to': [97], 'versions.': [103], 'results': [106, 150], 'show': [107, 134], 'that': [108], 'our': [109, 138, 155], 'algorithms': [113, 127, 142], 'can': [114], 'same': [117], 'convergence': [118], 'rates': [119], 'as': [120], 'ones': [122], 'exact': [124], 'setting.': [131], 'Finally,': [132], 'applications': [136], 'on': [143], 'representative': [145], 'Empirical': [149], 'confirm': [151], 'superiority': [153], 'new': [156], 'algorithms.': [160]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2963086517', 'counts_by_year': [{'year': 2024, 'cited_by_count': 2}, {'year': 2023, 'cited_by_count': 5}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 3}, {'year': 2019, 'cited_by_count': 6}, {'year': 2018, 'cited_by_count': 3}], 'updated_date': '2024-12-24T07:57:30.102255', 'created_date': '2019-07-30'}