Modified Wilson's Method for Nonlinear Programs with Nonunique Multipliers

Abstract

This paper first investigates Newton-type methods for generalized equations with compact solution sets. The analysis of their local convergence behavior is based, besides other conditions, on the upper Lipschitz-continuity of the local solution set mapping of a simply perturbed generalized equation. This approach is then applied to the KKT conditions of a nonlinear program with inequality constraints and leads to a modified version of the classical Wilson method. It is shown that the distances of the iterates to the set of KKT points converge q-quadratically to zero under conditions that do not imply a unique multiplier vector. Additionally to the Mangasarian-Fromovitz Constraint Qualification and to a Second-Order Sufficiency Condition the local minimizer is required to fulfill a Constant Rank Condition (weaker than the Constant Rank Constraint Qualification one of Janin) and a so-called Weak Complementarity Condition.