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Lagrange optimality system for a class of nonsmooth convex optimization

Jin, B; Takeuchi, T; (2015) Lagrange optimality system for a class of nonsmooth convex optimization. Optimization: A Journal of Mathematical Programming and Operations Research , 65 (6) pp. 1155-1166. 10.1080/02331934.2015.1101598. Green open access

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Abstract

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms: we derive a Lagrange–Newton algorithm for the nonsmooth convex optimization, and establish the nonsingularity of the Newton system and the local convergence of the algorithm.

Type: Article
Title: Lagrange optimality system for a class of nonsmooth convex optimization
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/02331934.2015.1101598
Publisher version: http://dx.doi.org/10.1080/02331934.2015.1101598
Language: English
Additional information: This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization: A Journal of Mathematical Programming and Operations Research on 19 October 2015, available online: http://www.tandfonline.com/10.1080/02331934.2015.1101598.
Keywords: nonsmooth convex optimization, augmented Lagrangian method, Lagrange optimality system, Newton method, 90C25, 46N10, 49M15
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1470815
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