On the R-superlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming

Ying Cui, Defeng Sun, Kim Chuan Toh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

Due to the possible lack of primal-dual-type error bounds, it was not clear whether the Karush–Kuhn–Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian method (ALM) for solving convex composite conic programming (CCCP) problems converge superlinearly. In this paper, we resolve this issue by establishing the R-superlinear convergence of the KKT residuals generated by the ALM under only a mild quadratic growth condition on the dual of CCCP, with easy-to-implement stopping criteria for the augmented Lagrangian subproblems. This discovery may help to explain the good numerical performance of several recently developed semismooth Newton-CG based ALM solvers for linear and convex quadratic semidefinite programming.

Original languageEnglish
Pages (from-to)381-415
Number of pages35
JournalMathematical Programming
Volume178
Issue number1-2
DOIs
Publication statusPublished - Nov 2019

Keywords

  • Augmented Lagrangian method
  • Convex composite conic programming
  • Implementable criteria
  • Quadratic growth condition
  • R-superlinear

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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