Duality in an Optimal Harvesting Problem by a Nonlinear Age-Spatial Structured Population Dynamic System

- Journal title : Kyungpook mathematical journal
- Volume 51, Issue 4, 2011, pp.353-364
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2011.51.4.353

Title & Authors

Duality in an Optimal Harvesting Problem by a Nonlinear Age-Spatial Structured Population Dynamic System

Kim, Yong-Kuk; Lee, Mi-Jin; Jung, Il-Hyo;

Kim, Yong-Kuk; Lee, Mi-Jin; Jung, Il-Hyo;

Abstract

Duality in the optimal harvesting for a nonlinear age-spatial structured population dynamic model is studied in the framework of optimal control problem. In this paper the duality theory that displays the conjugacy of the primal problem is established and an application is given. Duality theory plays an important role in both optimization theory and methodology and the results may be applied to a realistic biological system on the point of optimal harvesting.

Keywords

Duality theory;Optimal control problems;Age-structure;Harvesting problem;

Language

English

Cited by

References

1.

B. Ainseba, S. Anita and M. Langlais, Optimal control for a nonlinear age- structured population dynamics model, Electronic Journal of Differential Equations, 2002(28)(2002), 1-9.

2.

S. Anita, Optimal harvesting for a nonlinear age-dependent population dynamics, Journal of Mathematical Analysis and Applications, 226(1998), 6-22.

3.

Tadeusz Antczak, Optimal conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions, Journal of Computational and Applied Mathematics, 225(2009), 236-250.

4.

V. Barbu and M. Lannelli, Optimal control of population dynamics, Journal of Optimization Theory and Applications, 102(1)(1999), 1-14.

5.

F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, With 117 Illustrations, 2001 Springer-Verlag New York, Inc..

6.

A. V. Bulatov and V. F. Krotov, On dual problems of optimal control, Automation and Remote control, 69(10)(2008), 1653-1662.

7.

W. L. Chan, Duality in the optimal control of non-well-posed parabolic equations with positive control, Journal of Mathematical Analysis and Applications, 107(1985), 509-519.

8.

Nobuyuki Kato, Optimal harvesting for nonlinear size-structured population dynamics, Journal of Mathematical Analysis and Applications, 342(2008), 1388-1398.

9.

K. R. Fister and S. Lenhart, Optimal control of a competitive system with age- structure, Journal of Mathematical Analysis and Applications, 291(2004), 526-537.

10.

K. R. Fister and S. Lenhart, Optimal harvesting in an age-structured predatorprey model, Applied Mathematics and Optimization, 54(2006), 1-15.

11.

J. L. Lions, Optimal control of systems governed by partial differential equations, Springer-Verlag Berlin Heidelberg New York 1971.

12.

J. Y. Park and M. J. Lee, Duality in the optimal control problems for hyperbolic distributed parameter systems with damping terms, Journal of Mathematical Analysis and Applications, 227(1998), 449-461.

13.

J. Y. Park and M. J. Lee, Duality in the optimal control of distributed parameter systems governed by hyperbolic equations, Indian J. Pure Appl. Math., 31(4)(2000), 451-460.

14.

Y. H. Kang, J. B. Lee, M. J. Lee, Yongkuk Kim and I. H. Jung, Optimal harvesting for an age-spatial structured population model with an external environment, submitted for publication.

15.

S. Tanimoto, Duality in the optimal control of non-well-posed distributed systems, Journal of Mathematical Analysis and Applications, 171(1992), 277-287.

16.

G. Feichtinger, G. Tragler and V. M. Veliov, Optimal conditions for age-structured control systems, Journal of Mathematical Analysis and Applications, 95(1996), 25-42.