On the constrained error bound condition and the projected Levenberg–Marquardt method. (3rd August 2017)

• Record Type: Journal Article
• Authors: Behling, R.; Fischer, A.; Haeser, G.; Ramos, A.; Schönefeld, K.
• Is Part Of: Optimization. Volume 66:Number 8(2017)
• Page Start: 1397
• Page End: 1411
• Publication Date: 2017-08-03
• Subjects: Constrained equation -- differentiable manifold -- error bound -- nonisolated solution -- projected Levenberg–Marquardt method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1200578
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we first derive a characterization of the solution set of a continuously differentiable system of equations subject to a closed feasible set. Assuming that a constrained local error bound condition is satisfied, we prove that the solution set can locally be written as the intersection of a differentiable manifold with the feasible set. Based on the derivation of this result, we then show that the projected Levenberg–Marquardt method converges locally R-linearly to a possibly nonisolated solution under significantly weaker conditions than previously done.