DUALITY INEQUALITIES IN NONSMOOTH OPTIMIZATION
Herre Wiersma · Summit (Simon Fraser University) · 2002
Duality inequalities are pervasive in modern optimization; Fenchel duality and the MeanValue theorem are two prominent examples.This thesis surveys some recent duality results pertaining to nonsmooth functions, and examines some interesting corollaries thereof.One of these results is a somewhat surprising nonsmooth generalization of both the classical Mean Value theorem and the standard Fenchel duality theorem.Another gives rise to a variety of nonsmooth analogs to Rolle's theorem.Fixed point theory is central to the development of these results, and it is interesting to ask whether variational proofs might exist for some duality results.The answer to this question is mixed: some results admit variational proofs, whereas for others such a proof is unlikely.In particular, we show by counterexample that a certain Rolle-type duality theorem does not hold, even in EX2.my stay here a pleasant one, both academically and otherwise.Finally, I would like to thank my family and my girlfriend, Laurie, for helping me through a difficult year.