{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22664"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22664","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quasiconvex optimization via generalized gradients and symmetric duality","abstract":"Nondifferentiable quasiconvex programming problems are studied using Clarke's subgradients. Several conditions sufficient for optimality are derived. Under certain regularity conditions on the constraint functions, we also prove that a modified version of the classical Karush-Kuhn-Tucker conditions is both necessary and sufficient for optimality. The results extend and strengthen some by Arrow and Enthoven and by Mangasarian.","abstract_html":"Nondifferentiable quasiconvex programming problems are studied using Clarke's subgradients. Several conditions sufficient for optimality are derived. Under certain regularity conditions on the constraint functions, we also prove that a modified version of the classical Karush-Kuhn-Tucker conditions is both necessary and sufficient for optimality. The results extend and strengthen some by Arrow and Enthoven and by Mangasarian.","abstract_has_math":false,"creators":["Kugendran, Thambithurai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["McLinden, Lynn"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:47:18Z","date_published":"2011-05-07T13:47:18Z","updated_at":"2026-07-22T22:25:20Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1991 Kugendran, Thambithurai"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210879","(UMI)AAI9210879"],"render_values":[{"text":"AAI9210879","href":null,"code":true},{"text":"(UMI)AAI9210879","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22664","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McLinden, Lynn"]},{"key":"dc:creator","label":"Author","values":["Kugendran, Thambithurai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:47:18Z","10000-01-01","1991"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 Kugendran, Thambithurai"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210879","(UMI)AAI9210879","http://hdl.handle.net/2142/22664"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Nondifferentiable quasiconvex programming problems are studied using Clarke's subgradients. Several conditions sufficient for optimality are derived. Under certain regularity conditions on the constraint functions, we also prove that a modified version of the classical Karush-Kuhn-Tucker conditions is both necessary and sufficient for optimality. The results extend and strengthen some by Arrow and Enthoven and by Mangasarian.","In the second part, the Passy-Prisman symmetric perturbational duality scheme for quasiconvex minimization problems is developed in a manner that is more complete than that of Passy-Prisman. This scheme is then utilized to derive minimax results for quasisaddle functions, including in particular a slight extension of Sion's minimax theorem in finite dimensions. This approach to developing quasisaddle minimax results had been observed by Passy and Prisman, but their proofs had several crucial gaps. The development given here fills in the gaps and thus completes the proofs.","Made available in DSpace on 2011-05-07T13:47:18Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210879.pdf: 3595019 bytes, checksum: 1f0d33b8d8a69da42c2207772b45446f (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:59:10Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:27:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Quasiconvex optimization via generalized gradients and symmetric duality"]}]}],"canonical_facts":{"dc:contributor":["McLinden, Lynn"],"dc:creator":["Kugendran, Thambithurai"],"dc:date":["2011-05-07T13:47:18Z","10000-01-01","1991"],"dc:description":["Nondifferentiable quasiconvex programming problems are studied using Clarke's subgradients. Several conditions sufficient for optimality are derived. Under certain regularity conditions on the constraint functions, we also prove that a modified version of the classical Karush-Kuhn-Tucker conditions is both necessary and sufficient for optimality. The results extend and strengthen some by Arrow and Enthoven and by Mangasarian.","In the second part, the Passy-Prisman symmetric perturbational duality scheme for quasiconvex minimization problems is developed in a manner that is more complete than that of Passy-Prisman. This scheme is then utilized to derive minimax results for quasisaddle functions, including in particular a slight extension of Sion's minimax theorem in finite dimensions. This approach to developing quasisaddle minimax results had been observed by Passy and Prisman, but their proofs had several crucial gaps. The development given here fills in the gaps and thus completes the proofs.","Made available in DSpace on 2011-05-07T13:47:18Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210879.pdf: 3595019 bytes, checksum: 1f0d33b8d8a69da42c2207772b45446f (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:59:10Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:27:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9210879","(UMI)AAI9210879","http://hdl.handle.net/2142/22664"],"dc:language":["eng"],"dc:rights":["Copyright 1991 Kugendran, Thambithurai"],"dc:subject":["Mathematics"],"dc:title":["Quasiconvex optimization via generalized gradients and symmetric duality"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:20Z"}