## An inexact derivative-free Levenberg-Marquardt method for linear inequality constrained nonlinear systems under local error bound conditions.(English)Zbl 1410.49037

Summary: In this paper, a derivative-free affine scaling inexact Levenberg-Marquardt method with interior backtracking line search technique is considered for solving linear inequality constrained nonlinear systems. The proposed algorithm is designed to take advantage of the problem structure by building polynomial interpolation models for each function of nonlinear systems subject to the linear inequality constraints on variables. Each iterate switches to backtracking step generated by affine scaling inexact Levenberg-Marquardt method and satisfies strict interior point feasibility by line search backtracking technique. Under local error bounded assumption, the method is superlinear and quadratic convergent on $$F(x)$$. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

### MSC:

 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C56 Derivative-free methods and methods using generalized derivatives

levmar; WEDGE
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