Gauss Newton Method

Concept

solve

$$J^T(x_k)J(x_k)s_k=-J^T(x_k)r(x_k)$$ $$⟹J(x_k)s_k=-r(x_k)$$

instead of $H_f(x_k)s_k=-\nabla f(x_k)$ in Newton’s method.
It like Newton’s method applied to truncated Hessian matrix.