NDLI: On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating

Content Provider	Springer Nature Link
Author	Burke, J.V. Qian, Maijian
Copyright Year	2000
Abstract	In previous work, the authors provided a foundation for the theory of variable metric proximal point algorithms in Hilbert space. In that work conditions are developed for global, linear, and super–linear convergence. This paper focuses attention on two matrix secant updating strategies for the finite dimensional case. These are the Broyden and BFGS updates. The BFGS update is considered for application in the symmetric case, e.g., convex programming applications, while the Broyden update can be applied to general monotone operators. Subject to the linear convergence of the iterates and a quadratic growth condition on the inverse of the operator at the solution, super–linear convergence of the iterates is established for both updates. These results are applied to show that the Chen–Fukushima variable metric proximal point algorithm is super–linearly convergent when implemented with the BFGS update.
Starting Page	157
Ending Page	181
Page Count	25
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	88
Issue Number	1
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	2000-06-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating