Subdifferentials of marginal functions of parametric bang–bang control problems. (June 2020)

• Record Type: Journal Article
• Authors: Qui, Nguyen Thanh
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J61 -- 49J52 -- 49J53 -- 49K20 -- 49K30; Marginal function -- Bang–bang control -- Local upper weak-Hölderian selection -- Regular subdifferential -- Limiting Mordukhovich/singular subdifferential; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111743
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper investigates the differential stability of parametric bang–bang control problems governed by semilinear elliptic partial differential equations. Under some standard assumptions in optimal control theory, we establish exact formulas for computing the regular subdifferential, the Mordukhovich subdifferential, and the singular subdifferential of the marginal function of the parametric bang–bang control problems. The obtained results of subdifferential calculations deduce the local Lipschitzian property of the marginal function.