A globally and superlinearly convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations. (English) Zbl 0946.65031

Li, Donghui; Fukushima, Masao

SIAM J. Numer. Anal. 37, No. 1, 152-172 (1999).

The authors present a Gauss-Newton-based BFGS method for solving symmetric nonlinear equations which contain, as a special case, an unconstrained optimization problem, a saddle point problem, and an equality constrained optimization problem. A suitable line search is proposed with which the presented BFGS method exhibits an approximate norm descent property. Under appropriate conditions, global convergence and superlinear convergence of the method are established. The numerical results show that the proposed method is successful.

Reviewer: J.Guddat (Berlin)

MSC:

65H10	Numerical computation of solutions to systems of equations
65K05	Numerical mathematical programming methods
90C30	Nonlinear programming
90C26	Nonconvex programming, global optimization

Keywords:

BFGS method; global convergence; superlinear convergence; symmetric equations; Gauss-Newton method; unconstrained optimization; saddle point problem; constrained optimization; numerical results; line search

Software:

ve08