Li, Donghui; Fukushima, Masao A derivative-free line search and global convergence of Broyden-like method for nonlinear equations. (English) Zbl 0960.65076 Optim. Methods Softw. 13, No. 3, 181-201 (2000). 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. Reviewer: Iulian Coroian (Baia Mare) Cited in 7 ReviewsCited in 86 Documents 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 Keywords:derivative-free line search; quasi-Newton methods; global convergence; superlinear convergence; symmetric nonlinear equations; nonlinear programming; Broyden-like method; numerical results × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1090/S0025-5718-1965-0198670-6 · doi:10.1090/S0025-5718-1965-0198670-6 [2] DOI: 10.1093/imamat/12.3.223 · Zbl 0282.65041 · doi:10.1093/imamat/12.3.223 [3] DOI: 10.1090/S0025-5718-1974-0343581-1 · doi:10.1090/S0025-5718-1974-0343581-1 [4] DOI: 10.1137/1019005 · Zbl 0356.65041 · doi:10.1137/1019005 [5] DOI: 10.1017/S0334270000005208 · Zbl 0596.65034 · doi:10.1017/S0334270000005208 [6] DOI: 10.1007/BF01385810 · Zbl 0724.90060 · doi:10.1007/BF01385810 [7] Li D.H., SIAM J. Numer. Anal 59 (1991) [8] DOI: 10.1080/01630569908816921 · Zbl 0934.65123 · doi:10.1080/01630569908816921 [9] Li D.H., Broyden-like methods for variational inequality and nonlinear complementarity problems with global and superlinear convergence (1998) [10] Li D.H., Comput. Optim. Appl (1998) [11] Li D.H., A nonsmooth equation based BFGS method for solving KKT systems in mathematical programming (1998) [12] Ortega J.M., Iterative Solution of Nonlinear Equations in Several Variables (1970) · Zbl 0241.65046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.