Lagrange optimality system for a class of nonsmooth convex optimization. (2nd June 2016)

• Record Type: Journal Article
• Authors: Jin, B.; Takeuchi, T.
• Is Part Of: Optimization. Volume 65:Number 6(2016)
• Page Start: 1151
• Page End: 1166
• Publication Date: 2016-06-02
• Subjects: nonsmooth convex optimization -- augmented Lagrangian method -- Lagrange optimality system -- Newton method; 90C25 -- 46N10 -- 49M15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1101598
• Languages: English
• ISSNs: 0233-1934

Abstract

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.