The Piecewise Levenberg–Marquardt Method

Abstract

We develop sharp local superlinear convergence results for the Levenberg–Marquardt method applied to constrained piecewise smooth equations, under the local Lipschitzian error bound condition for active selections, allowing for nonisolated solutions. We also characterize the level of inexactness allowed when solving subproblems, such that it does not interfere with superlinear convergence rate. Applications to constrained reformulations of complementarity systems, using the “min” complementarity function are also discussed.