Author:
Banert Sebastian,Boţ Radu Ioan,Csetnek Ernö Robert
Abstract
AbstractWe investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269–297, 2014) in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration, we allow the use of variable metrics, while the investigations are carried out in the setting of infinite-dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.
Publisher
Springer Science and Business Media LLC
Reference30 articles.
1. Alotaibi, A., Combettes, P. L., Shahzad, N.: Solving coupled composite monotone inclusions by successive Fejér approximations of their Kuhn-Tucker set. SIAM J. Optim. 24(4), 2076–2095 (2014)
2. Attouch, H., Soueycatt, M.: Augmented Lagrangian and proximal alternating direction methods of multipliers in Hilbert spaces. Applications to games, PDE’s and control. Pacific J. Optim. 5, 17–37 (2009)
3. Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd edn. CMS Books in Mathematics, Springer, New York (2017)
4. Borwein, J. M., Vanderwerff, J. D.: Convex Functions: Constructions, Characterizations and Counterexamples. Cambridge University Press, Cambridge (2010)
5. Boţ, R.I.: Conjugate Duality in Convex Optimization Lecture Notes in Economics and Mathematical Systems, vol. 637. Springer, Berlin (2010)
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