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

Nguyen Huy Chieu (), Nguyen Thi Quynh Trang () and Ha Anh Tuan ()
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Nguyen Huy Chieu: Vinh University
Nguyen Thi Quynh Trang: Vinh University
Ha Anh Tuan: Ho Chi Minh City University of Transport

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 14, 1106 pages

Abstract: Abstract 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.

Keywords: Quadratic growth; Strong metric subregularity; Second-order differentiability in the extended sense; Second-order epi-differentiability; Prox-regularity; 49J53; 90C31; 90C46 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02071-6

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