The Piecewise Levenberg–Marquardt Method
Keywords:
nonlinear equation, constrained equation, piecewise smooth equation, nonisolated solution, local error bound, 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.
Published
2024-04-02
Section
Articles