zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The optimal strategy for a bioeconomical model of a harvesting renewable resource problem. (English) Zbl 1077.91036
Authors summary: In recent years, bioeconomics has seen fast development in different areas of natural resource modelling. In this paper, we study a bioeconomic model, where the control is the fishing effort variation rate, rather than the effort in the classical model of Clark, which can be interpreted as an investment. This consideration leads to a nonlinear problem of optimal control. We first establish a result on stability of the equilibrium point. We also obtain the optimal strategy of the model by applying the inductive method based on the verification functions.

91B76Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90Applications of optimal control and differential games
91B62Growth models in economics
Full Text: DOI
[1] Clarke, F. H.; Ledyaev, Y. S.; Strem, R. J.; Wolenski, P. R.: Nonsmooth analysis and optimal control theory. Graduate texts in mathematics 178 (1998)
[2] Clark, C. W.: Second edition the optimal management of renewable resources, mathematical bioeconomics. The optimal management of renewable resources, mathematical bioeconomics (1990) · Zbl 0712.90018
[3] Clark, C. W.; Munro, G.: The economics of fishing and modern capital theory: A simplified approach. J. environmental econom. And management 2, 92-106 (1975)
[4] Schäefer, M. B.: Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bulletin of the inter-American tropical tuna commission 1, 25-26 (1954)
[5] Pella, J. J.; Tomlinson, P. K.: A generalized stock production model. Bulletin of the inter-American tropical tuna commission 13, 421-496 (1969)
[6] Clarke, F. H.: Optimization and nonsmooth analysis. (1983) · Zbl 0582.49001
[7] Clarke, F. H.: Methods of dynamics and nonsmooth optimization. (1990) · Zbl 0696.49002
[8] De Pinho, M. Do Rosario; Vinter, R. B.: An Euler-Lagrange inclusion for optimal control problems. IEEE transactions on automatic control 40, No. 7 (1995) · Zbl 0827.49014
[9] Rockafellar, R. T.: Equivalent subgradient version of Hamiltonian and Euler-Lagrange equation in variational analysis. SIAM J. Control optim 34, 1300-1314 (1996) · Zbl 0878.49012
[10] Clarke, F. H.; Ledyanuv, Y. S.; Sontag, E. D.; Subbotin, A. I.: Asymptotic controllability implies feedback stabilization. IEEE transactions on automatic control 20, No. Y (1999)
[11] Clark, C. W.; Clarke, F. H.; Munro, G.: The optimal management of renewable resources stocks: problem of irreversible investment. Econometrica 47, 25-47 (1979) · Zbl 0396.90026
[12] Arnold, V.: Third edition equations differentielles ordinaires. Equations differentielles ordinaires (1974)
[13] Lyon, K.: The costate variable in natural resource optimal control problems. Presented at 1997 world conference on natural resource modeling (December 15--18, 1997)
[14] Kaitala, V.; Munro, G.: The conservation and management of high seas fishery resources under the new law of the sea. Natural resource modeling 10, No. 2 (1997) · Zbl 0927.91031
[15] Touzeau, S.: Modèle de contrôle en gestion des pêches. Thèse (1997)