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Second-Order Epi-Derivatives of Composite Functionals



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.



Annals of Operations ResearchSpringer Journals

Published: Jan 1, 2001

DOI: 10.1023/A:1010993128564

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