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An affine scaling interior Levenberg-Marquardt method for KKT systems. (English) Zbl 1299.90379

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
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