Quasi-Newton methods for generalized equations

Norman Josephy (1)

1 Department of Mathematics [Madison]

Newton's method is a well known and often applied technique for computing a zero of a nonlinear function. Situations arise in which it is undesirable to evaluate, at each iteration, the derivative appearing in the Newton iteration formula. In these cases, a technique of much modern interest is the quasi-Newton method, in which an approximation to the derivative is used in place of the derivative. By using the theory of generalized equations, quasi-Newton methods are developed to solve problems arising in both mathematical programming and mathematical economics. We prove two results concerning the convergence and convergence rate of quasi-Newton methods for generalized equations. We present computational results of quasi-Newton methods applied to a nonlinear complementarity problem of Kojima.

Mots clés: Variational Inequalities; Complementarity; Quasi-Newton Methods

Domaines: Mathématiques [math]

Norman Josephy. Quasi-Newton methods for generalized equations. [Research Report] University of Wisconsin. 1979. ⟨hal-01316084⟩