Inexact Restoration Methods for Nonlinear Programming: Advances and Perspectives

Abstract

Inexact Restoration methods have been introduced in the last few years for solving nonlinear programming problems. These methods are related to classical restoration algorithms but also have some remarkable differences. They generate a sequence of generally infeasible iterates with intermediate iterations that consist of inexactly restored points. The convergence theory allows one to use arbitrary algorithms for performing the restoration. This feature is appealing because it allows one to use the structure of the problem in quite opportunistic ways. Different Inexact Restoration algorithms are available. The most recent ones use the trust-region approach. However, unlike the algorithms based on sequential quadratic programming, the trust regions are centered not in the current point but in the inexactly restored intermediate one. Global convergence has been proved, based on merit functions of augmented Lagrangian type. In this survey we point out some applications and we relate recent advances in the theory.