The proximal point algorithm without monotonicity
2023-11 | conference paper. A publication with affiliation to the University of Göttingen.
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The proximal point algorithm without monotonicity
Luke, D. R. & Tam, M. K. (2023)
In:Liu, Tianxiang; Yamashita, Makoto (Eds.), Proceedings of the 35th RAMP Mathematical Optimization Symposium pp. 39-48. 35th RAMP Mathematical Optimization Symposium, Tokyo.
Tokyo: Research Association of Mathematical Programming.
Documents & Media
Details
- Authors
- Luke, D. Russell ; Tam, Matthew K.
- Editors
- Liu, Tianxiang; Yamashita, Makoto
- Corporate Editor
- Research Association of Mathematical Programming
- Abstract
- We study the proximal point algorithm in the setting in which the operator of inter- est is metrically subregular and satisfies a submonoticity property. The latter can be viewed as a quantified weakening of the standard definition of a monotone operator. Our main result gives a condition under which, locally, the proximal point algorithm generates at least one sequence which is linearly convergent to a zero of the underlying operator. General properties of our notion of submonotonicity are also explored as well as connections to other concepts in the literature.
- Issue Date
- November-2023
- Status
- In Press
- Publisher
- Research Association of Mathematical Programming
- Project
- SFB 1456 | Cluster B | B01: Mathematics of atomic orbital tomography
- Organization
- Institut für Numerische und Angewandte Mathematik
- Working Group
- RG Luke (Continuous Optimization, Variational Analysis and Inverse Problems)
- Conference
- 35th RAMP Mathematical Optimization Symposium
- Conference Place
- Tokyo
- Event start
- 2023-11-20
- Event end
- 2023-11-17
- Language
- English
- Subject(s)
- submonotone; proximal point algorithm; metric subregularity; almost α-firmly non- expansive; monotone; hypomonotone
