Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #98006 (February, 1998)

A Globally and Superlinearly Convergent Gauss-Newton Based BFGS Method for Symmetric Equations
by Donghui Li and Masao Fukushima

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.