A Survey of Multi - step Quasi -

Quasi-Newton methods have been utilized as a standard technique for solving nonlinear optimization problems and nonlinear systems of equations for over thirty years. These methods, in almost all cases, make use of data obtained from the step just completed in the variable space to revise the current approximation to the Hessian / Jacobian. Recently, a new class of multi-step quasi-Newton methods has been introduced, in which (by contrast) data from more than one previous step is used in revising the approximation. We describe the fundamental process by which these methods are derived, and then go on to discuss some of the techniques by means of which the exibility inherent in this derivation may be exploited to produce subclasses of multi-step methods with speciic properties. We conclude with a brief survey of some numerical experiments on these methods.