A derivative-free line search and global convergence of Broyden-like method for nonlinear equations. (English) Zbl 0960.65076

The purpose of this paper is to propose a quasi-Newton method with a well-defined derivative-free line search and to study global and superlinear convergence of this method. For a special type of equation, an equation involving a mapping with positive definite Jacobian matrix, the authors propose a norm descent quasi-Newton method and prove its global and superlinear convergence. The numerical results show that the algorithm performs quite well for the tested problems.


65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
90C53 Methods of quasi-Newton type
90C56 Derivative-free methods and methods using generalized derivatives
Full Text: DOI


[1] DOI: 10.1090/S0025-5718-1965-0198670-6 · doi:10.1090/S0025-5718-1965-0198670-6
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