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

• Published in: Journal of optimization theory and applications Vol. 194; no. 3; pp. 1081 - 1106
• Main Authors: Chieu, Nguyen Huy, Trang, Nguyen Thi Quynh, Tuan, Ha Anh
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2022; Springer Nature B.V
• 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; 90C31; Quadratic growth; 49J53; 90C46; Strong metric subregularity; Second-order epi-differentiability; Second-order differentiability in the extended sense; Prox-regularity
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-022-02071-6

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.