  Nonlinear least-squares problems are a special class of unconstrained
optimization problems in which their gradient and Hessian have special
structures. In this paper, we exploit these structures and proposed a
matrix-free algorithm with a diagonal Hessian approximation for solving
nonlinear least-squares problems. We devise appropriate safeguarding strategies
to ensure the Hessian matrix is positive definite throughout the iteration
process. The proposed algorithm generates descent direction and is globally
convergent. Preliminary numerical experiments show that the proposed method is
competitive with a recently developed similar method.
