A new line search inexact restoration approach for nonlinear programming

A new general scheme for Inexact Restoration methods for Nonlinear Programming is introduced. After computing an inexactly restored point, the new iterate is determined in an approximate tangent affine subspace by means of a simple line search on a penalty function. This differs from previous method...

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Bibliographic Details
Published in:Computational optimization and applications 2010-06, Vol.46 (2), p.333-346
Main Authors: Fischer, Andreas, Friedlander, Ana
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Convex and Discrete Geometry
Linear programming
Management Science
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Studies
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Summary:A new general scheme for Inexact Restoration methods for Nonlinear Programming is introduced. After computing an inexactly restored point, the new iterate is determined in an approximate tangent affine subspace by means of a simple line search on a penalty function. This differs from previous methods, in which the tangent phase needs both a line search based on the objective function (or its Lagrangian) and a confirmation based on a penalty function or a filter decision scheme. Besides its simplicity the new scheme enjoys some nice theoretical properties. In particular, a key condition for the inexact restoration step could be weakened. To some extent this also enables the application of the new scheme to mathematical programs with complementarity constraints.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-009-9267-0