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Improved local convergence results for augmented Lagrangian methods in \({\varvec{C}}^\mathbf{2}\)-cone reducible constrained optimization

  • Christian Kanzow
  • Daniel Steck
Short Communication Series A
  • 108 Downloads

Abstract

This paper deals with a class of cone-reducible constrained optimization problems which encompasses nonlinear programming, semidefinite programming, second-order cone programming, and any combination thereof. Using the second-order sufficient condition and a strict version of the Robinson constraint qualification, we provide a (semi-)local error bound which generalizes known results from the literature. Moreover, under the same assumptions, we prove that an augmented Lagrangian method is locally convergent with rate proportional to \(1/\rho _k\), where \(\rho _k\) is the penalty parameter, and that \(\{\rho _k\}\) remains bounded.

Keywords

Augmented Lagrangian method Local convergence Rate of convergence \(C^2\)-cone reducible sets Error bound Semidefinite programming Second-order cone programming 

Mathematics Subject Classification

65K05 90C22 90C30 90C31 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of Würzburg, Campus Hubland NordWürzburgGermany

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