Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions

This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially continuous, prox-regular, twice epi-differentiable function. For...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2022-09, Vol.194 (3), p.1081-1106
Main Authors: Chieu, Nguyen Huy, Trang, Nguyen Thi Quynh, Tuan, Ha Anh
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Continuity (mathematics)
Engineering
Euclidean space
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
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Summary:This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially continuous, prox-regular, twice epi-differentiable function. For such a function, which is not necessarily prox-regular, it is shown that the quadratic growth, the strong metric subregularity of the subdifferential at a local minimizer, and the positive definiteness of the subgradient graphical derivative at a stationary point are equivalent. In addition, other characterizations of the quadratic growth and the strong metric subregularity of the subdifferential are also given. Besides, properties of functions twice differentiable in the extended sense are examined.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02071-6