Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints. (10th October 2022)

• Record Type: Journal Article
• Authors: Kien, B. T.; Tuan, N. Q.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 14(2022)
• Page Start: 1672
• Page End: 1706
• Publication Date: 2022-10-10
• Subjects: Convergence -- error estimate -- finite element method -- first-and second-order optimality conditions -- optimal control -- semilinear elliptic equation; 49K20 -- 35J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2124271
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This paper gives some sufficient conditions for convergence of approximate solutions to seminlinear elliptic optimal control problems with mixed pointwise constraints. We build discrete optimal control problems by the finite element method in type of the full control discretization. We show that if the strictly second-order sufficient condition is valid, then some error estimates between approximate solutions of discrete optimal control problems and optimal solutions of the original problem are obtained.