Department of Applied Mathematics & Physics, Kyoto Univiversity
Technical Report #98010 (April, 1998)
A Derivative-Free Line Search and DFP Method for Symmetric Equations with Global and Superlinear Convergence
by Donghui Li and Masao Fukushima
In this paper, we propose a derivative-free line search suited to
iterative methods for solving
systems of nonlinear equations with symmetric Jacobian matrices.
The proposed line search can be implemented conveniently
by a backtracking process
and has such an
that any iterative method with this line search generates a sequence of
iterates that is
approximately norm descent. Moreover, if the Jacobian matrices are
uniformly nonsingular, then the generated
sequence converges to the unique solution.
We incorporate this line search
with a Gauss-Newton based DFP method
for solving symmetric equations.
Under appropriate conditions, we establish
global and superlinear convergence of the proposed DFP method.
The obtained results show, in particular, that
the proposed DFP method with inexact line search converges globally and
superlinearly even for nonconvex unconstrained optimization problems
and equality constrained optimization problems.