Variations of structured Broyden families for nonlinear least squares problems, Optimization Methods and

In this paper, we consider methods for finding a local solution, $x^{*} $ say, to a nonlinear least squares problem (1) minimize $f(x) = \frac{1}{2}\sum_{j=1}^{m}(r_{j}(x))^{2} $, where $r_{j} $ : $R^{n}arrow R, $ $j=1, $ $\ldots, $ $m(m\geq n) $ are twice continuously differentiable. Such problem