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Second-Order Epi-Derivatives of Composite Functionals

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  • A.B. Levy

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

Suggested Citation

  • A.B. Levy, 2001. "Second-Order Epi-Derivatives of Composite Functionals," Annals of Operations Research, Springer, vol. 101(1), pages 267-281, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:267-281:10.1023/a:1010993128564
    DOI: 10.1023/A:1010993128564
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