Newton's method for generalized equations: a sequential implicit function theorem

In the extension of Newton’s method to generalized equations, applying to variational inequalities as a special case, convergence analysis relates to a corresponding implicit function theorem, describes how solutions may depend on a parameter. In this paper the implicit function paradigm is carried further and placed in the framework of a mapping from the parameter to sequence of iterates as elements of a sequence space, Key Words. Newton’s method, generalized equations, variational inequalities, strong regularity, implicit function theorems, inverse function theorems, perturbations, variational analysis.

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Asen L. Dontchev, R. Tyrrell Rockafellar
• Keywords: Function Theorems, Implicit Function, MP 2010, Variational Inequalities