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An extension of the proximal point algorithm beyond convexity
- Source :
- Journal of Global Optimization, Journal of Global Optimization, Springer Verlag, 2021, ⟨10.1007/s10898-021-01081-4⟩
- Publication Year :
- 2021
-
Abstract
- We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however none of these classes fully contains the one of prox-convex functions or is included into it. We show that the classical proximal point algorithm remains convergent when the convexity of the proper lower semicontinuous function to be minimized is relaxed to prox-convexity.
- Subjects :
- Control and Optimization
Nonsmooth optimization
0211 other engineering and technologies
Mathematics::Optimization and Control
010103 numerical & computational mathematics
02 engineering and technology
Management Science and Operations Research
01 natural sciences
Convexity
Quasiconvex function
Operator (computer programming)
FOS: Mathematics
Mathematics - Numerical Analysis
0101 mathematics
Mathematics - Optimization and Control
Mathematics
021103 operations research
Applied Mathematics
Regular polygon
Function (mathematics)
Extension (predicate logic)
Numerical Analysis (math.NA)
Computer Science Applications
Proximal point
Nonconvex optimization
Generalized convex function
Proximity operator
Optimization and Control (math.OC)
Proximal point algorithm
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithm
Subjects
Details
- Language :
- English
- ISSN :
- 09255001 and 15732916
- Database :
- OpenAIRE
- Journal :
- Journal of Global Optimization, Journal of Global Optimization, Springer Verlag, 2021, ⟨10.1007/s10898-021-01081-4⟩
- Accession number :
- edsair.doi.dedup.....61a8086a0ec87b2b04c0181b2468f6e9