Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity

Ahookhosh, Masoud, Aragón Artacho, Francisco J., Fleming, Ronan M.T. and Vuong, Phan T. (2019) Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity. Advances in Computational Mathematics, 1-36. (doi:10.1007/s10444-019-09708-7).

Record type: Article

Abstract

We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt parameter and analyse the local convergence of the method under Hölder metric subregularity of the function defining the equation and Hölder continuity of its gradient mapping. Further, we analyse the local convergence of the method under the additional assumption that the Łojasiewicz gradient inequality holds. We finally report encouraging numerical results confirming the theoretical findings for the problem of computing moiety conserved steady states in biochemical reaction networks. This problem can be cast as finding a solution of a system of nonlinear equations, where the associated mapping satisfies the Łojasiewicz gradient inequality assumption.

Text

Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity - Accepted Manuscript

Available under License University of Southampton Accepted Manuscript Licence.

Download (1MB)

Text

Ahookhosh2019_Article_LocalConvergenceOfTheLevenberg - Version of Record

Restricted to Repository staff only

Request a copy