Sensitivity analysis of solutions to generalized equations

Generalized equations are common in the study of optimization through nonsmooth analysis. For instance, variational inequalities can be written as generalized equations involving normal cone mappings, and have been used to represent first-order optimality conditions associated with optimization problems. Therefore, the stability of the solutions to first-order optimality conditions can be determined from the differential properties of the solutions of parameterized generalized equations. In finite-dimensions, solutions to parameterized variational inequalities are known to exhibit a type of generalized differentiability appropriate for multifunctions. Here it is shown, in a Banach space setting, that solutions to a much broader class of parameterized generalized equations are "differentiable" in a similar sense.