A globally convergent BFGS method for symmetric nonlinear equations | Zendy

Weijun Zhou | Zendy

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A globally convergent BFGS method for symmetric nonlinear equations

Author(s) -

Weijun Zhou

Publication year - 2021

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2021020

Subject(s) - broyden–fletcher–goldfarb–shanno algorithm , jacobian matrix and determinant , iterative method , matrix (chemical analysis) , mathematics , local convergence , quasi newton method , gaussian elimination , nonlinear system , newton's method , computer science , mathematical optimization , gaussian , physics , computer network , materials science , asynchronous communication , quantum mechanics , composite material

A BFGS type method is presented to solve symmetric nonlinear equations, which is shown to be globally convergent under suitable conditions. Compared with some existing Gauss-Newton-based BFGS methods whose iterative matrix approximates the Gauss-Newton matrix, an important feature of the proposed method lies in that the iterative matrix is an approximation of the Jacobian, which greatly reduces condition number of the iterative matrix. Numerical results are reported to support the theory.

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