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.
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Levy, A. Second-Order Epi-Derivatives of Composite Functionals. Annals of Operations Research 101, 267–281 (2001). https://doi.org/10.1023/A:1010993128564
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DOI: https://doi.org/10.1023/A:1010993128564