Wang, Yunjuan; Zhu, Detong An affine scaling interior Levenberg-Marquardt method for KKT systems. (English) Zbl 1299.90379 Oper. Res. Trans. 17, No. 2, 89-106 (2013). Summary: We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving Karush-Kuhn-Tucker (KKT) systems. By transforming the KKT system into an equivalent minimization problem with nonnegativity constraints on some of the variables, we establish the Levenberg-Marquardt equation based on this reformulation. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local superlinear convergent rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. MSC: 90C51 Interior-point methods 65K10 Numerical optimization and variational techniques Keywords:KKT systems; Levenberg-Marquardt method; affine scaling; interior point; convergence PDFBibTeX XMLCite \textit{Y. Wang} and \textit{D. Zhu}, Oper. Res. Trans. 17, No. 2, 89--106 (2013; Zbl 1299.90379)