Inexact-Restoration methods for nonlinear programming: Advances and Perspectives

JOSÉ MARIO MARTÍNEZ; ELVIO A. PILOTTA

Optimization and Control with Applications. (Applied Optimization Series, V. 96)

Springer

Lugar: New York; Año: 2005; p. 271 - 292

Abstract.Inexact Restoration methods have been introduced in the last few yearsfor solving nonlinear programming problems.  These methods are relatedto  classical restoration  algorithms  but also  have some  remarkabledifferences.   They  generate   a  sequence  of  generally  infeasibleiterates  with  intermediate  iterations  that  consist  of  inexactlyrestored points.   The convergence theory allows one  to use arbitraryalgorithms for performing the  restoration.  This feature is appealingbecause it  allows one to  use the structure  of the problem  in quiteopportunistic  ways.   Different  Inexact Restoration  algorithms  areavailable.   The  most  recent  ones use  the  trust-region  approach.However,   unlike  the  algorithms   based  on   sequential  quadraticprogramming, the trust  regions are centered not in  the current pointbut in  the inexactly  restored intermediate one.   Global convergencehas  been proved,  based on  merit functions  of  augmented Lagrangiantype.  In  this survey  we point out  some applications and  we relaterecent advances in the theory.