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Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming.

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Title: Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming.
Authors: Cafieri, S.1 sonia.cafieri@unina2.it, D'Apuzzo, M.1, De Simone, V.1, di Serafino, D.1, Toraldo, G.2
Source: Journal of Optimization Theory & Applications. Dec2007, Vol. 135 Issue 3, p355-366. 12p. 1 Chart.
Subjects: Stochastic convergence, Quadratic programming, Duality theory (Mathematics), Interior-point methods, Mathematical programming, Factorization, Algorithms
Abstract: We analyze the convergence of an infeasible inexact potential reduction method for quadratic programming problems. We show that the convergence of this method is achieved if the residual of the KKT system satisfies a bound related to the duality gap. This result suggests stopping criteria for inner iterations that can be used to adapt the accuracy of the computed direction to the quality of the potential reduction iterate in order to achieve computational efficiency. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & 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.)
Database: Engineering Source
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  Data: Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming.
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  Data: <searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
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  Data: We analyze the convergence of an infeasible inexact potential reduction method for quadratic programming problems. We show that the convergence of this method is achieved if the residual of the KKT system satisfies a bound related to the duality gap. This result suggests stopping criteria for inner iterations that can be used to adapt the accuracy of the computed direction to the quality of the potential reduction iterate in order to achieve computational efficiency. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Optimization Theory & 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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        Value: 10.1007/s10957-007-9264-3
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        Text: English
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        Type: general
      – SubjectFull: Quadratic programming
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      – SubjectFull: Duality theory (Mathematics)
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      – SubjectFull: Interior-point methods
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      – SubjectFull: Mathematical programming
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      – SubjectFull: Factorization
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      – SubjectFull: Algorithms
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      – TitleFull: Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming.
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              Text: Dec2007
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