Zhao, Ruixue; Fan, Jinyan Global complexity bound of the Levenberg-Marquardt method. (English) Zbl 1406.65037 Optim. Methods Softw. 31, No. 4, 805-814 (2016). Summary: In this paper, we propose a new updating rule of the Levenberg-Marquardt (LM) parameter for the LM method for nonlinear equations. We show that the global complexity bound of the new LM algorithm is \(O(\varepsilon^{-2})\), that is, it requires at most \(O(\varepsilon^{-2})\) iterations to derive the norm of the gradient of the merit function below the desired accuracy \(\varepsilon\). Cited in 13 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:nonlinear equations; Levenberg-Marquardt method; global complexity bound PDFBibTeX XMLCite \textit{R. Zhao} and \textit{J. Fan}, Optim. Methods Softw. 31, No. 4, 805--814 (2016; Zbl 1406.65037) Full Text: DOI References: [1] DOI: 10.1007/s10107-009-0337-y · Zbl 1229.90193 · doi:10.1007/s10107-009-0337-y [2] Fan J.Y., J. Comput. Math. 21 pp 625– (2003) [3] Fan J.Y., Appl. Math. Comput. 207 pp 351– (2009) · Zbl 1172.65024 · doi:10.1016/j.amc.2008.10.056 [4] DOI: 10.1007/s00607-004-0083-1 · Zbl 1076.65047 · doi:10.1007/s00607-004-0083-1 [5] DOI: 10.1007/s10107-014-0794-9 · Zbl 1319.90065 · doi:10.1007/s10107-014-0794-9 [6] Moré J.J., Numer. Anal. 630 pp 105– (1978) [7] DOI: 10.1080/08927020600643812 · Zbl 1136.65051 · doi:10.1080/08927020600643812 [8] DOI: 10.1017/S033427000000120X · Zbl 0364.90100 · doi:10.1017/S033427000000120X [9] DOI: 10.1007/s00245-009-9094-9 · Zbl 1228.90087 · doi:10.1007/s00245-009-9094-9 [10] DOI: 10.1007/s10957-010-9731-0 · Zbl 1203.90152 · doi:10.1007/s10957-010-9731-0 [11] DOI: 10.1007/s10957-011-9907-2 · Zbl 1250.90116 · doi:10.1007/s10957-011-9907-2 [12] DOI: 10.1017/S0334270000004604 · Zbl 0574.65059 · doi:10.1017/S0334270000004604 [13] Yamashita N., Computing (Supplement) 15 pp 237– (2001) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.