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McLinden, Lynn Kugendran, Thambithurai 2011-05-07T13:47:18Z 2011-05-07T13:47:18Z 10000-01-01 1991 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 AAI9210879 (UMI)AAI9210879 http://hdl.handle.net/2142/22664 eng Copyright 1991 Kugendran, Thambithurai Mathematics Quasiconvex optimization via generalized gradients and symmetric duality text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.