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 writ ten as generalized equations involving normal cone mappings, and have been used to represent first-order optimality conditions associated wi th optimization problems. Therefore, the stability of the solutions to first-order optimality conditions can be determined from the differen tial properties of the solutions of parameterized generalized equation s. In finite-dimensions, solutions to parameterized variational inequa lities are known to exhibit a type of generalized differentiability ap propriate for multifunctions. Here it is shown, in a Banach space sett ing, that solutions to a much broader class of parameterized generaliz ed equations are ''differentiable'' in a similar sense.