Second-order epi-derivatives of composite functionals

We compute two-sided second-order epi-derivatives for certain composite fun ctionals f = g o 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 minim ization problems on Banach spaces. Our proof relies on our development of a formula for the second-order upper epi-derivative that mirrors a formula f or a second-order lower epi-derivative from [7], and the two-sided results we obtain promise to support a more precise sensitivity analysis of paramet erized optimization problems than has been previously possible.