Local behavior of an iterative framework for generalized equations with nonisolated solutions

An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations with the structure 0 F(z) + T (z), where T is a multifunction and F is singlevalued, the framework covers methods that, at each step, solve subproblems of the type 0 A(z, s) + T (z). The multifunction A approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution set map of the perturbed generalized equation 0 F(z) + T (z) + p. Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising from nonlinear programs, and nonlinear equations. Particular results deal with err...

• Type: Journal
• Year: 2002
• Where: MP
• Authors: Andreas Fischer
• Keywords: Generalized Equation, MP 2002, Solutions, Upper Lipschitz-continuity