Least squares updates for quasi-Newton methods in process design and simulation

Abstract

A least squares updating formula is proposed for use in quasi-Newton methods to solve systems of full nonlinear equations more effectively and reliably. Two updating schemes are derived by applying the method of exponentially weighted least squares to the quasi-Newton and Newton's iteration equation, respectively. Each new formula requires an additional symmetric matrix, which, however, provides some information about when to reset the method. Thus, the nonself-correctiveness problems of the existing quasi-Newton methods can be partially resolved without any other resetting procedure. Numerical results on several standard test problems show that the proposed methods are more reliable and efficient than the well-known Broyden method.