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Stopping criteria for inner iterations in inexact potential reduction methods: a computational study.

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Title: Stopping criteria for inner iterations in inexact potential reduction methods: a computational study.
Authors: Cafieri, S.1 sonia.cafieri@unina2.it, D'Apuzzo, M.1 marco.dapuzzo@unina2.it, De Simone, V.1 valentina.desimone@unina2.it, Di Serafino, D.1 daniela.diserafino@unina2.it
Source: Computational Optimization & Applications. Mar2007, Vol. 36 Issue 2/3, p165-193. 29p. 7 Charts, 8 Graphs.
Subjects: Iterative methods (Mathematics), Numerical analysis, Quadratic programming, Nonlinear programming, Mathematics, Stochastic convergence
Abstract: We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required. [ABSTRACT FROM AUTHOR]
Copyright of Computational Optimization & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Computational+Optimization+%26+Applications%22">Computational Optimization & Applications</searchLink>. Mar2007, Vol. 36 Issue 2/3, p165-193. 29p. 7 Charts, 8 Graphs.
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  Data: We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Optimization & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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