A secant method for nonlinear least-squares minimization

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance (e.g., Dennis and Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, 1996). In addition, most modern optimization libraries house a quasi-Newton collection of codes and they are widely used. The quasi-Newton contribution to practical nonlinear optimization is unchallenged.