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Lapin, A. and Laitinen, E. (2018) Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation. Journal of Applied Mathematics and Physics, 6, 58-68. https://doi.org/10.4236/jamp.2018.61007

Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation

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Author: Lapin, A.1,2; Laitinen, E.3
Organizations: 1Institute of Computational Mathematics & Information Technology, Kazan Federal University, Kazan, Russia
2Tianjin University of Finance and Economics, Tianjin , China
3Department of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Persistent link: http://urn.fi/urn:nbn:fi-fe201901293404
Language: English
Published: Scientific Research Publishing, 2018
Publish Date: 2019-01-29
Description:

Abstract

We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.

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Series: Journal of applied mathematics and physics
ISSN: 2327-4352
ISSN-E: 2327-4379
ISSN-L: 2327-4352
Volume: 6
Issue: 1
Article number: 81585
DOI: 10.4236/jamp.2018.61007
OADOI: https://oadoi.org/10.4236/jamp.2018.61007
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Constrained Saddle Point Problem
Finite Difference Method
Iterative Method
Parabolic Optimal Control
State Constraints
Article
Funding: The research was supported by the RFBR grant No. 16-01-00408 and by grants No. 296348 and No. 296928 from Academy of Finland.
Academy of Finland Grant Number: 296348
296928
Detailed Information: 296348 (Academy of Finland Funding decision)
296928 (Academy of Finland Funding decision)
Copyright information: © 2018 The Authors. CC-BY.
  https://creativecommons.org/licenses/by/4.0/