Article

Annals of Operations Research

, Volume 101, Issue 1, pp 267-281

Second-Order Epi-Derivatives of Composite Functionals

  • A.B. LevyAffiliated withDepartment of Mathematics, Bowdoin College

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Abstract

We compute two-sided second-order epi-derivatives for certain composite functionals f=gF 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