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Journal of Optimization Theory and Applications

, Volume 175, Issue 2, pp 450–477 | Cite as

Stability and Accuracy of Inexact Interior Point Methods for Convex Quadratic Programming

  • Benedetta MoriniEmail author
  • Valeria Simoncini
Article

Abstract

We consider primal–dual interior point methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation and different processes for retrieving the step after block elimination. Our analysis is general and includes as special cases sources of inexactness due either to roundoff and computational errors or to the iterative solution of the augmented system using typical procedures. In the roundoff case, we recover and extend some known results.

Keywords

Convex quadratic programming Primal–dual interior point methods Inexact interior point steps 

Mathematics Subject Classification

65K05 90C51 90C06 

Notes

Acknowledgements

This work was partially supported by INdAM-GNCS under the 2016 Project Metodi numerici per problemi di ottimizzazione vincolata di grandi dimensioni e applicazioni.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Università degli Studi di FirenzeFlorenceItaly
  2. 2.Università di BolognaBolognaItaly
  3. 3.IMATI-CNRPaviaItaly

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