, Volume 101, Issue 1, pp 267281
First online:
SecondOrder EpiDerivatives of Composite Functionals
 A.B. LevyAffiliated withDepartment of Mathematics, Bowdoin College
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We compute twosided secondorder epiderivatives 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 realvalued 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 secondorder upper epiderivative that mirrors a formula for a secondorder lower epiderivative from [7], and the twosided results we obtain promise to support a more precise sensitivity analysis of parameterized optimization problems than has been previously possible.
 Title
 SecondOrder EpiDerivatives of Composite Functionals
 Journal

Annals of Operations Research
Volume 101, Issue 14 , pp 267281
 Cover Date
 200101
 DOI
 10.1023/A:1010993128564
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 secondorder epiderivative
 twice Mosco epidifferentiability
 convexC 2 composite function
 Industry Sectors
 Authors

 A.B. Levy ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, USA