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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Published in | Journal of optimization theory and applications Vol. 194; no. 3; pp. 1081 - 1106 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.09.2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0022-3239 1573-2878 |
DOI: | 10.1007/s10957-022-02071-6 |