Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2100384283', 'doi': 'https://doi.org/10.1007/s10957-009-9525-4', 'title': 'New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization', 'display_name': 'New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization', 'publication_year': 2009, 'publication_date': '2009-02-26', 'ids': {'openalex': 'https://openalex.org/W2100384283', 'doi': 'https://doi.org/10.1007/s10957-009-9525-4', 'mag': '2100384283'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s10957-009-9525-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S52430896', 'display_name': 'Journal of Optimization Theory and Applications', 'issn_l': '0022-3239', 'issn': ['0022-3239', '1573-2878'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5050992508', 'display_name': 'C. Gutiérrez', 'orcid': 'https://orcid.org/0000-0002-8223-2088'}, 'institutions': [{'id': 'https://openalex.org/I108103353', 'display_name': 'Universidad de Valladolid', 'ror': 'https://ror.org/01fvbaw18', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I108103353']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'C. Gutiérrez', 'raw_affiliation_strings': ['Universidad de Valladolid ,'], 'affiliations': [{'raw_affiliation_string': 'Universidad de Valladolid ,', 'institution_ids': ['https://openalex.org/I108103353']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5069972821', 'display_name': 'Bienvenido Jiménez', 'orcid': 'https://orcid.org/0000-0003-1513-8590'}, 'institutions': [{'id': 'https://openalex.org/I178450904', 'display_name': 'National University of Distance Education', 'ror': 'https://ror.org/02msb5n36', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I178450904']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'B. Jiménez', 'raw_affiliation_strings': ['Universidad Nacional de Educación a Distancia.'], 'affiliations': [{'raw_affiliation_string': 'Universidad Nacional de Educación a Distancia.', 'institution_ids': ['https://openalex.org/I178450904']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5001299859', 'display_name': 'Vicente Novo', 'orcid': 'https://orcid.org/0000-0001-9033-3180'}, 'institutions': [{'id': 'https://openalex.org/I178450904', 'display_name': 'National University of Distance Education', 'ror': 'https://ror.org/02msb5n36', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I178450904']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'V. Novo', 'raw_affiliation_strings': ['Universidad Nacional de Educación a Distancia.'], 'affiliations': [{'raw_affiliation_string': 'Universidad Nacional de Educación a Distancia.', 'institution_ids': ['https://openalex.org/I178450904']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2390, 'currency': 'EUR', 'value_usd': 2990, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 2.102, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 31, 'citation_normalized_percentile': {'value': 0.925458, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 91, 'max': 92}, 'biblio': {'volume': '142', 'issue': '1', 'first_page': '85', 'last_page': '106'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10545', 'display_name': 'Optimization and Variational Analysis', 'score': 0.9999, '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'}}, 'topics': [{'id': 'https://openalex.org/T10545', 'display_name': 'Optimization and Variational Analysis', 'score': 0.9999, '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'}}, {'id': 'https://openalex.org/T10963', 'display_name': 'Advanced Optimization Algorithms Research', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11115', 'display_name': 'Topology Optimization in Engineering', 'score': 0.9928, 'subfield': {'id': 'https://openalex.org/subfields/2205', 'display_name': 'Civil and Structural Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/directional-derivative', 'display_name': 'Directional derivative', 'score': 0.83244944}, {'id': 'https://openalex.org/keywords/theory-of-computation', 'display_name': 'Theory of computation', 'score': 0.606658}, {'id': 'https://openalex.org/keywords/fréchet-derivative', 'display_name': 'Fréchet derivative', 'score': 0.5697556}, {'id': 'https://openalex.org/keywords/derivative', 'display_name': 'Derivative (finance)', 'score': 0.49563968}, {'id': 'https://openalex.org/keywords/material-derivative', 'display_name': 'Material derivative', 'score': 0.41854024}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.85292995}, {'id': 'https://openalex.org/C2011187', 'wikidata': 'https://www.wikidata.org/wiki/Q383851', 'display_name': 'Directional derivative', 'level': 2, 'score': 0.83244944}, {'id': 'https://openalex.org/C164088818', 'wikidata': 'https://www.wikidata.org/wiki/Q7917833', 'display_name': 'Vector optimization', 'level': 4, 'score': 0.69412935}, {'id': 'https://openalex.org/C57691317', 'wikidata': 'https://www.wikidata.org/wiki/Q1289248', 'display_name': 'Scalar (mathematics)', 'level': 2, 'score': 0.64561427}, {'id': 'https://openalex.org/C24858836', 'wikidata': 'https://www.wikidata.org/wiki/Q844718', 'display_name': 'Theory of computation', 'level': 2, 'score': 0.606658}, {'id': 'https://openalex.org/C118335899', 'wikidata': 'https://www.wikidata.org/wiki/Q1305350', 'display_name': 'Fréchet derivative', 'level': 3, 'score': 0.5697556}, {'id': 'https://openalex.org/C202615002', 'wikidata': 'https://www.wikidata.org/wiki/Q783507', 'display_name': 'Differentiable function', 'level': 2, 'score': 0.5577874}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.5489911}, {'id': 'https://openalex.org/C137836250', 'wikidata': 'https://www.wikidata.org/wiki/Q984063', 'display_name': 'Optimization problem', 'level': 2, 'score': 0.5447453}, {'id': 'https://openalex.org/C182306322', 'wikidata': 'https://www.wikidata.org/wiki/Q1779371', 'display_name': 'Order (exchange)', 'level': 2, 'score': 0.5429276}, {'id': 'https://openalex.org/C126255220', 'wikidata': 'https://www.wikidata.org/wiki/Q141495', 'display_name': 'Mathematical optimization', 'level': 1, 'score': 0.51146615}, {'id': 'https://openalex.org/C111771559', 'wikidata': 'https://www.wikidata.org/wiki/Q66295', 'display_name': 'Derivative (finance)', 'level': 2, 'score': 0.49563968}, {'id': 'https://openalex.org/C33257320', 'wikidata': 'https://www.wikidata.org/wiki/Q1932744', 'display_name': 'Second derivative', 'level': 2, 'score': 0.4805577}, {'id': 'https://openalex.org/C184537036', 'wikidata': 'https://www.wikidata.org/wiki/Q14163503', 'display_name': 'Generalizations of the derivative', 'level': 3, 'score': 0.4694364}, {'id': 'https://openalex.org/C111915175', 'wikidata': 'https://www.wikidata.org/wiki/Q1801562', 'display_name': 'Material derivative', 'level': 2, 'score': 0.41854024}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.33696786}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.10991329}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.07405144}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.07076618}, {'id': 'https://openalex.org/C122357587', 'wikidata': 'https://www.wikidata.org/wiki/Q6934508', 'display_name': 'Multi-swarm optimization', 'level': 3, 'score': 0.06434533}, {'id': 'https://openalex.org/C10138342', 'wikidata': 'https://www.wikidata.org/wiki/Q43015', 'display_name': 'Finance', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C106159729', 'wikidata': 'https://www.wikidata.org/wiki/Q2294553', 'display_name': 'Financial economics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s10957-009-9525-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S52430896', 'display_name': 'Journal of Optimization Theory and Applications', 'issn_l': '0022-3239', 'issn': ['0022-3239', '1573-2878'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://econpapers.repec.org/RePEc:spr:joptap:v:142:y:2009:i:1:d:10.1007_s10957-009-9525-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306401271', 'display_name': 'RePEc: Research Papers in Economics', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I77793887', 'host_organization_name': 'Federal Reserve Bank of St. Louis', 'host_organization_lineage': ['https://openalex.org/I77793887'], 'host_organization_lineage_names': ['Federal Reserve Bank of St. Louis'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 26, 'referenced_works': ['https://openalex.org/W113278869', 'https://openalex.org/W1495508859', 'https://openalex.org/W1551360398', 'https://openalex.org/W1582299569', 'https://openalex.org/W1585268704', 'https://openalex.org/W1601741115', 'https://openalex.org/W195337544', 'https://openalex.org/W1966587106', 'https://openalex.org/W1972720745', 'https://openalex.org/W1975211588', 'https://openalex.org/W1990592299', 'https://openalex.org/W1995576098', 'https://openalex.org/W2001933474', 'https://openalex.org/W2017898167', 'https://openalex.org/W2019915680', 'https://openalex.org/W2022828798', 'https://openalex.org/W2027449074', 'https://openalex.org/W2041037772', 'https://openalex.org/W2045544449', 'https://openalex.org/W2117463942', 'https://openalex.org/W2149537314', 'https://openalex.org/W2802620382', 'https://openalex.org/W4249125060', 'https://openalex.org/W46032731', 'https://openalex.org/W50621378', 'https://openalex.org/W585047121'], 'related_works': ['https://openalex.org/W4299507264', 'https://openalex.org/W2973604913', 'https://openalex.org/W2963067150', 'https://openalex.org/W2376373908', 'https://openalex.org/W2364861597', 'https://openalex.org/W2351274863', 'https://openalex.org/W2196251960', 'https://openalex.org/W2100384283', 'https://openalex.org/W2097846334', 'https://openalex.org/W2064205779'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2100384283', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 3}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 3}, {'year': 2017, 'cited_by_count': 4}, {'year': 2016, 'cited_by_count': 3}, {'year': 2014, 'cited_by_count': 3}, {'year': 2013, 'cited_by_count': 2}, {'year': 2012, 'cited_by_count': 4}], 'updated_date': '2024-12-10T00:46:26.164631', 'created_date': '2016-06-24'}