, Volume 1, Issue 4, pp 379392
First online:
Secondorder epiderivatives of integral functionals
 A. B. LevyAffiliated withDepartment of Mathematics, University of Washington
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Epiderivatives have many applications in optimization as approached through nonsmooth analysis. In particular, secondorder epiderivatives can be used to obtain optimality conditions and carry out sensitivity analysis. Therefore the existence of secondorder epiderivatives for various classes of functions is a topic of considerable interest. A broad class of composite functions on ℝ^{ n } called ‘fully amenable’ functions (which include general penalty functions composed withC ^{2} mappings, possibly under a constraint qualification) are now known to be twice epidifferentiable. Integral functionals appear widely in problems in infinitedimensional optimization, yet to date, only integral functionals defined by convex integrands have been shown to be twice epidifferentiable, provided that the integrands are twice epidifferentiable. Here it is shown that integral functionals are twice epidifferentiable even without convexity, provided only that their defining integrands are twice epidifferentiable and satisfy a uniform lower boundedness condition. In particular, integral functionals defined by fully amenable integrands are twice epidifferentiable under mild conditions on the behavior of the integrands.
Mathematics Subject Classifications (1991)
Primary: 49J52 Secondary: 58C20Key words
Generalized second derivatives nonsmooth analysis epiderivatives fully amenable functions integral functionals optimization Title
 Secondorder epiderivatives of integral functionals
 Journal

SetValued Analysis
Volume 1, Issue 4 , pp 379392
 Cover Date
 199312
 DOI
 10.1007/BF01027827
 Print ISSN
 09276947
 Online ISSN
 1572932X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Primary: 49J52
 Secondary: 58C20
 Generalized second derivatives
 nonsmooth analysis
 epiderivatives
 fully amenable functions
 integral functionals
 optimization
 Authors

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

 1. Department of Mathematics, University of Washington, 98195, Seattle, WA, U.S.A.