A Globally and Superlinearly Convergent Gauss--Newton-Based BFGS Method for Symmetric Nonlinear Equations

In this paper, we 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.