Quasiconvex optimization via generalized gradients and symmetric duality
Kugendran, Thambithurai
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https://hdl.handle.net/2142/22664
Description
Title
Quasiconvex optimization via generalized gradients and symmetric duality
Author(s)
Kugendran, Thambithurai
Issue Date
1991
Doctoral Committee Chair(s)
McLinden, Lynn
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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.
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