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 single-valued, 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 fom nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity properties for these problems.
