University of Oulu

Pyy, J.; Ahtikoski, A.; Lapin, A.; Laitinen, E. Solution of Optimal Harvesting Problem by Finite Difference Approximations of Size-Structured Population Model. Math. Comput. Appl. 2018, 23, 22.

Solution of optimal harvesting problem by finite difference approximations of size-structured population model

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Author: Pyy, Johanna1; Ahtikoski, Anssi2; Lapin, Alexander3;
Organizations: 1Faculty of Sciences, University of Oulu, FI-90014 Oulu, Finland
2Natural Resources Institute Finland (Luke) Oulu, FI-90014 Oulu, Finland
3Institute of Computational Mathematics & Information Technology, Kazan Federal University, 420008 Kazan, Russia
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.8 MB)
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Language: English
Published: Multidisciplinary Digital Publishing Institute, 2018
Publish Date: 2019-01-29


We solve numerically a forest management optimization problem governed by a nonlinear partial differential equation (PDE), which is a size-structured population model. The formulated problem is supplemented with a natural constraint for a solution to be non-negative. PDE is approximated by an explicit or implicit in time finite difference scheme, whereas the cost function is taken from the very beginning in the finite-dimensional form used in practice. We prove the stability of the constructed nonlinear finite difference schemes on the set of non-negative vectors and the solvability of the formulated discrete optimal control problems. The gradient information is derived by constructing discrete adjoint state equations. The projected gradient method is used for finding the extremal points. The results of numerical testing for several real problems show good agreement with the known results and confirm the theoretical statements.

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Series: Mathematical and computational applications
ISSN: 2297-8747
ISSN-E: 2297-8747
ISSN-L: 2297-8747
Volume: 23
Issue: 2
Article number: 22
DOI: 10.3390/mca23020022
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (