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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.

MSC:
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
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