Duality Inequalities in Nonsmooth Optimization

Wiersma, Herre (2003) Duality Inequalities in Nonsmooth Optimization. MSc Thesis thesis, Simon Fraser University.

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      Duality inequalities are pervasive in modern optimization; Fenchel duality and the Mean Value 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 $\R^2$.

      Item Type: Thesis (MSc Thesis)
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: duality, nonsmooth optimization, Rolle's theorem, Lewis-Ralph sandwich theorems, Clarke-Ledyaev mean value inequality
      Subjects: UNSPECIFIED
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Oct 2003
      Last Modified: 21 Apr 2010 11:13

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