FEM for Semilinear Elliptic Optimal Control with Nonlinear and Mixed Constraints

Bui Trong Kien (), Arnd Rösch (), Nguyen Hai Son () and Nguyen Van Tuyen ()
Additional contact information
Bui Trong Kien: Vietnam Academy of Science and Technology
Arnd Rösch: University of Duisbug-Essen
Nguyen Hai Son: Hanoi University of Science and Technology
Nguyen Van Tuyen: Hanoi Pedagogical University 2

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 1, No 6, 130-173

Abstract: Abstract This paper studies the convergence and error estimates of approximate solutions to an optimal control problem governed by semilinear elliptic equations with non-convex cost function and non-convex mixed pointwise constraints, and unbounded constraint set. We discretize the optimal control problems by the finite element method in order to obtain a sequence of mathematical programming problems in finite-dimensional spaces. We show that under certain conditions, the optimal solutions of the obtained mathematical programming problems converge to an optimal solution of the original problem. In particular, if the original problem satisfies the so-called no-gap second-order conditions, then some error estimates of approximate solutions are obtained.

Keywords: Finite element method; Optimal control; Semilinear elliptic equation; First-and second-order optimality conditions; Convergence; Error estimate; 49K20; 35J25 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-023-02187-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02187-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-023-02187-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().