Second-Order Epi-Derivatives of Composite Functionals Authors A.B. Levy Department of Mathematics Bowdoin College Article

DOI :
10.1023/A:1010993128564

Cite this article as: Levy, A. Annals of Operations Research (2001) 101: 267. doi:10.1023/A:1010993128564
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.

second-order epi-derivative
twice Mosco epi-differentiability
convex-C
^{2} composite function

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© Kluwer Academic Publishers 2001