Second-Order Epi-Derivatives of Composite Functionals

A.B. Levy ()

Annals of Operations Research, 2001, vol. 101, issue 1, 267-281

Abstract: We compute two-sided second-order epi-derivatives for certain composite functionals f=g○F where F is a C 1 mapping between two Banach spaces X and Y, and g is a convex extended real-valued function on Y. These functionals include most essential objectives associated with smooth constrained minimization problems on Banach spaces. Our proof relies on our development of a formula for the second-order upper epi-derivative that mirrors a formula for a second-order lower epi-derivative from [7], and the two-sided results we obtain promise to support a more precise sensitivity analysis of parameterized optimization problems than has been previously possible. Copyright Kluwer Academic Publishers 2001

Keywords: second-order epi-derivative; twice Mosco epi-differentiability; convex-C 2 composite function (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1010993128564

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