The Josephy--Newton method for semismooth generalized equations and semismooth SQP for optimization
M.V. Solodov | Izmailov, A.F. | Kurennoy, A.S.
While generalized equations with differentiable single-valued base mappings and the associated Josephy--Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush-Kuhn-Tucker optimality systems). We introduce for the general semismooth case appropriate notions of solution regularity and prove local convergence of the corresponding Josephy--Newton method. As an application, we immediately recover the known primal-dual local convergence properties of semismooth SQP, but also obtain some new results that complete the analysis of the SQP primal rate of convergence, including its quasi-Newton variant.