Augmented Lagrangian method for second-order cone programs under second-order sufficiency

This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact forms. Using generalized differential tools of second-order var...

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Bibliographic Details
Published in:Journal of global optimization 2022, Vol.82 (1), p.51-81
Main Authors: Hang, Nguyen T. V., Mordukhovich, Boris S., Sarabi, M. Ebrahim
Format: Article
Language:English
Subjects:
Computer Science
Equality
Lagrange multiplier
Mathematical functions
Mathematical optimization
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Real Functions
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Summary:This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact forms. Using generalized differential tools of second-order variational analysis, we formulate the corresponding version of second-order sufficiency and use it to establish, among other results, the uniform second-order growth condition for the augmented Lagrangian. The latter allows us to justify the solvability of subproblems in the ALM and to prove the linear primal–dual convergence of this method.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01068-1