Annals of Operations Research

, Volume 101, Issue 1–4, pp 267–281

Second-Order Epi-Derivatives of Composite Functionals

  • A.B. Levy

DOI: 10.1023/A:1010993128564

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


We compute two-sided second-order epi-derivatives for certain composite functionals f=gF where F is a C1 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-C2 composite function 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A.B. Levy
    • 1
  1. 1.Department of MathematicsBowdoin CollegeBrunswickUSA

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