Issue
Math. Model. Nat. Phenom.
Volume 14, Number 1, 2019
Economics and the environment: distributed optimal control models
Article Number 106
Number of page(s) 14
DOI https://doi.org/10.1051/mmnp/2019016
Published online 27 May 2019
  1. R. Adams, S. Hamilton and B. McCarl, The benefits of pollution control: the case of ozone and U.S. agriculture. Am. J. Agric. Econ. 68 (1986) 886–893. [Google Scholar]
  2. H. Amann, Dynamic theory of quasilinear parabolic systems. Math. Z. 202 (1989) 219–250. [CrossRef] [Google Scholar]
  3. H. Amann, Dynamic theory of quasilinear parabolic systems. Math. Z. 205 (1990) 331–331. [CrossRef] [Google Scholar]
  4. S. Aniţa and V. Arnautu, Some aspects concerning the optimal harvesting problem. Sci. Annals Univ. “Ion Ionescu de la Brad” Iatsi 48 (2005) 65–73. [Google Scholar]
  5. S. Aniţa, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics, From Mathematical Models to Numerical Simulation with MATLAB, Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (2010). [Google Scholar]
  6. S. Aniţa, V. Arnăutu and R. Ştefănescu, Numerical optimal harvesting for a periodic age-structured population dynamics with logistic term. Numer. Funct. Anal. Optim. 30 (2009) 183–198. [Google Scholar]
  7. S. Aniţa, S. Behringer, A.M. Mosneagu and T. Upmann, Optimal harvesting of a spatially distributed renewable resource with endogenous pricing. In: Special issue Economics and the environment: distributed optimal control models. MMNP 14 (2019) 101. [EDP Sciences] [Google Scholar]
  8. L.I. Aniţa, V. Capasso and A.M. Mosneagu, Optimal harvesting for periodic age-dependent population dynamics. SIAM J. Appl. Math. 58 (1998) 1648–1666. [Google Scholar]
  9. L.I. Aniţa, V. Capasso and A.M. Mosneagu, Regional control in optimal harvesting of population dynamics. Nonlinear Anal. 147 (2016) 191–212. [CrossRef] [Google Scholar]
  10. L.I. Aniţa, M. Iannelli, M.Y. Kim and E.J. Park, Optimal harvesting for periodic age-dependent population dynamics. SIAM J. Appl. Math. 58 (1998) 1648–1666. [Google Scholar]
  11. S.M. Aseev and A.V. Kryazhimskii, The Pontryagin maximum principle and transversality conditions for a class optimal control problems with infinite time horizons. SIAM J. Control Optim. 43 (2004) 1094–1119. [CrossRef] [Google Scholar]
  12. S. Aseev and V. Veliov, Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions. Proc. Steklov Inst. Math. 291 (2015) 22–39. [CrossRef] [Google Scholar]
  13. E. Augeraud-Véron, C. Choquet and E.́ Comte, Optimal control for a groundwater pollution ruled by a convection–diffusion–reaction problem. J. Optim. Theory Appl. 173 (2017) 941–966. [Google Scholar]
  14. E. Augeraud-Véron and A. Ducrot, Spatial externality and intederminacy. In: Special issue Economics and the environment: distributed optimal control models. MMNP 14 (2019) 102. [EDP Sciences] [Google Scholar]
  15. L.V. Ballestra, The spatial AK model and the Pontryagin maximum principle. J. Math. Econ. 67 (2016) 87–94. [Google Scholar]
  16. V. Barbu and M. Iannelli, Optimal control of population dynamics. J. Optim. Theory Appl. 102 (1999) 1–14. [Google Scholar]
  17. E. Barucci and F. Gozzi, Technology adoption and accumulation in a vintage-capital model. J. Econ. 74 (2001) 1–38. [CrossRef] [Google Scholar]
  18. S. Behringer and T. Upmann, Optimal harvesting of a spatial renewable resource. J. Econ. Dyn. Control 42 (2014) 105–120. [Google Scholar]
  19. M. Belhachemi and F. Addoun, Comparative adsorption isotherms and modeling of methylene blue onto activated carbons. Appl. Water Sci. 1 (2011) 111–117. [Google Scholar]
  20. A.O. Belyakov, A.A. Davydov and V.M. Veliov, Optimal cyclic exploitation of renewable resources. J. Dyn. Control Syst. 21 (2015) 475–494. [Google Scholar]
  21. A. Belyakov and V.M. Veliov, Constant versus periodic fishing: age structured optimal control approach. MMNP 9 (2014) 20–38. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  22. A.O. Belyakov and V.M. Veliov, On optimal harvesting in age-structured populations, in Dynamic Perspectives on Managerial Decision Making – Essays in Honor of Richard Hartl, edited by H. Dawid et al. Springer, Switzerland (2016) 149–166. [Google Scholar]
  23. C. Benosman, B. Aïnseba and A. Ducrot, Optimization of cytostatic leukemia therapy in an advection-reaction-diffusion model. J.Optim. Theory Appl. 167 (2014) 296–325. [CrossRef] [Google Scholar]
  24. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Springer Science and Business Media, Berlin (2007). [CrossRef] [Google Scholar]
  25. R. Boucekkine, C. Camacho and G. Fabbri, Spatial dynamics and convergence: the spatial AK model. J. Econ. Theory 148 (2013) 2719–2736. [Google Scholar]
  26. R. Boucekkine, C. Camacho and G. Fabbri, On the optimal control of some parabolic partial differential equations arising in economics (Special issue in honor of Vladimir Veliov). Serdica Math. J. 39 (2013) 1001–1024. [Google Scholar]
  27. R. Boucekkine, G. Fabbri and F. Gozzi, Egalitarianism under population change: age structure does matter. J. Math. Econ. 55 (2014) 86–100. [Google Scholar]
  28. R. Boucekkine, G. Fabbri, S. Federico and F. Gozzi, Geographic environmental Kuznets curves: the optimal growth linear-quadratic case. In: Special issue Economics and the environment: distributed optimal control models. MMNP 14 (2019) 105. [EDP Sciences] [Google Scholar]
  29. R. Boucekkine, G. Fabbri, S. Federico and F. Gozzi, Growth and agglomeration in the heterogeneous space: a generalized AK approach. To appear in: J. Econ. Geogr. (2018) lby041. Doi: 10.1093/jeg/lby041. [Google Scholar]
  30. M. Braack, M.F. Quaas, B. Tews and B. Vexler, Optimization of fishing strategies in space and time as a non-convex optimal control problem. J. Optim. Theory Appl. (2018) 1–23. [Google Scholar]
  31. A. Bressan, G.M. Coclite and W. Shen, A multidimensional optimal-harvesting problem with measure-valued solutions. SIAM J. Control Optim. 51 (2013) 1186–1202. [CrossRef] [Google Scholar]
  32. P. Brito, The dynamics of growth and distribution in a spatially heterogeneous world. Working Papers Department of Economics 2004-14. ISEG, University of Lisbon (2004). [Google Scholar]
  33. W. Brock and A. Xepapadeas, Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control. J. Econ. Dyn. Control 32 (2008) 2745–2787. [Google Scholar]
  34. W. Brock, A. Xepapadeas and A.N. Yannacopoulos, Optimal control in space and time and the management of environmental resources. Annu. Rev. Resour. Econ. 6 (2014) 33–68. [CrossRef] [Google Scholar]
  35. M. Brokate, Pontryagin’s principle for control problems in age-dependent population dynamics. J. Math. Biol. 23 (1985) 75–101. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. C. Camacho and A. Pérez-Barahona, Land use dynamics and the environment. J. Econ. Dyn. Control 52 (2015) 96–118. [Google Scholar]
  37. C. Camacho and A. Pérez-Barahona, A model in continuous time and space to study economic migration. In: Special issue Economics and the environment: distributed optimal control models. MMNP 14 (2019) 103. [EDP Sciences] [Google Scholar]
  38. D.A. Carlson, A.B. Haurie and A. Leizarowitz, Infinite Horizon Optimal Control: Deterministic and Stochastic Systems. Springer, Berlin (1991). [CrossRef] [Google Scholar]
  39. C. Choquet, E. Augeraud-Véron and E. Comte, Existence, uniqueness and asymptotic analysis of optimal control problems for a model of groundwater pollution. To appear in: ESAIM: COCV (2018). DOI: 10.1051/cocv/2018041. [Google Scholar]
  40. G.M. Coclite and M. Garavello, A time-dependent optimal harvesting problem with measure-valued solutions. SIAM J. Control Optim. 55 (2017) 913–935. [CrossRef] [Google Scholar]
  41. J. de Frutos and G. Martín-Herrán, Spatial effects and strategic behavior in a multiregional transboundary pollution dynamic game. J. Environ. Econ. Manag. (2017). [Google Scholar]
  42. J. de Frutos and G. Martín-Herrán, Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games. To appear in: Eur. J. Oper. Res. (2017). Doi: 10.1016/j.jeem.2017.08.001. [Google Scholar]
  43. G. Fabbri, Geographical structure and convergence: a note on geometry in spatial growth models. J. Econ. Theory 162 (2016) 114–136. [Google Scholar]
  44. G. Fabbri and F. Gozzi, Solving optimal growth models with vintage capital: the dynamic programming approach. J. Econ. Theory 143 (2008) 331–373. [Google Scholar]
  45. G. Fabbri, F. Gozzi and A. Swiech, Stochastic Optimal Control in Infinite Dimension: Probability and Stochastic Modelling. Springer, Switzerland (2017). [CrossRef] [Google Scholar]
  46. H.O. Fattorini, Infinite Dimensional Optimization and Control Theory. Cambridge University Press, Cambridge (1999). [CrossRef] [Google Scholar]
  47. G. Feichtinger, G. Tragler and V.M. Veliov, Optimality conditions for age-structured control systems. J. Math. Anal. Appl. 288 (2003) 47–68. [Google Scholar]
  48. G. Feichtinger, Ts. Tsachev and V.M. Veliov, Maximum principle for age and duration structured systems: a tool for optimal prevention and treatment of HIV. Math. Popul. Stud. 11 (2004) 3–28. [Google Scholar]
  49. G. Feichtinger and V.M. Veliov, On a distributed control problem arising in dynamic optimization of a fixed-size population. SIAM J. Optim. 18 (2007) 980–1003. [Google Scholar]
  50. M. Fujita and J. Thisse, Economics of Agglomeration. Cambridge University Press, Cambridge (2013). [CrossRef] [Google Scholar]
  51. P. Golubtsov and S.I. Steinshamn, Analytical and numerical investigation of optimal harvesting with a continuously age-structured model. Ecol. Modell. 392 (2019) 67–81. [Google Scholar]
  52. D. Grass, J.P. Caulkins, G. Feichtinger, G. Tragler and D.A. Behrens, Optimal Control of Nonlinear Processes, with Applications in Drugs, Corruption and Terror. Springer, Berlin (2011). [Google Scholar]
  53. D. Grass and H. Uecker, Optimal management and spatial patterns in a distributed shallow lake model. Electron. J. Differ. Equ. 2017 (2017) 1–21. [CrossRef] [Google Scholar]
  54. D. Grass, H. Uecker and T. Upmann, Optimal Fishery with Coastal Catch (2018). [Google Scholar]
  55. H. Halkin, Necessary conditions for optimal control problems with infinite horizons. Econometrica 42 (1974) 267–272. [Google Scholar]
  56. Z.R. He and R. Liu, Theory of optimal harvesting for a nonlinear size-structured population in periodic environments. Int. J. Biomath. 7 (2014) 1–18. [Google Scholar]
  57. H.R. Joshi, G.E. Herrera, S. Lenhart and M.G. Neubert. Optimal dynamic harvest of a mobile renewable resource. Nat. Resour. Model. 22 (2009) 322–343. [Google Scholar]
  58. I. Kan, A. Leizerovitz and Y. Tsur, Dynamic-spatial management of coastal aquifers. Optim. Control Appl. Meth. 31 (2009) 29–41. [Google Scholar]
  59. M.R. Kelly, Jr., Y. Xing and S. Lenhart, Optimal fish harvesting for a population modeled by a nonlinear parabolic partial differential equation. Nat. Res. Model. 29 (2016) 36–70. [CrossRef] [Google Scholar]
  60. P. Landi, C. Hui and U. Dieckmann, Fisheries-induced disruptive selection. J. Theor. Biol. 365 (2015) 204–216. [CrossRef] [PubMed] [Google Scholar]
  61. D. La Torre, D. Liuzzi and S. Marsiglio, The optimal population size under pollution and migration externalities: a spatial control approach. A model in continuous time and space to study economic migration. In: Special issue Economics and the environment: distributed optimal control models. MMNP 14 (2019) 104. [EDP Sciences] [Google Scholar]
  62. X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems. Birkhäuser, Boston (1995). [CrossRef] [Google Scholar]
  63. Z. Luo, W.T. Li and M. Wang, Optimal harvesting control problem for linear periodic age-dependent population dynamics. Appl. Math. Comput. 151 (2004) 789–800. [Google Scholar]
  64. F. Mariani, A. Pérez-Barahona and N. Raffin, Life expectancy and the environment. J. Econ. Dyn. Control 34 (2010) 798–815. [Google Scholar]
  65. P. Michel, On the trasversality condition in infinite horizon optimal problems. Econometrica 50 (1982) 975–985. [Google Scholar]
  66. P. Mossay, Increasing returns and heterogeneity in a spatial economy. Reg. Sci. Urban Econ. 33 (2003) 419–444. [Google Scholar]
  67. C. Simon, B. Skritek and V.M. Veliov, Optimal immigration age-patterns in populations of fixed size. J. Math. Anal. Appl. 405 (2013) 71–89. [Google Scholar]
  68. B. Skritek and V.M. Veliov, On the infinite-horizon optimal control of age-structured systems. J. Optim. Theory Appl. 167 (2015) 243–271. [Google Scholar]
  69. O. Tahvonen, Optimal harvesting of age-structured fish populations. Mar. Resour. Econ. 24 (2009) 147–169. [CrossRef] [Google Scholar]
  70. N. Tauchnitz, The Pontryagin maximum principle for nonlinear optimal control problems with infinite horizon. J. Optim. Theory Appl. 167 (2015) 27–48. [Google Scholar]
  71. F. Tröltzsch, Optimal Control of Partial Differential Equations, Vol. 112 of Graduate Studies in Mathematics. AMS, RI (2010). [CrossRef] [Google Scholar]
  72. H. Uecker, Optimal harvesting and spatial patterns in a semiarid vegetation system. Nat. Resour. Model. 29 (2016) 229–258. [Google Scholar]
  73. V.M. Veliov, Optimal control of heterogeneous systems: basic theory. J. Math. Anal. Appl. 346 (2008) 227–242. [Google Scholar]
  74. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, New York (1985). [Google Scholar]

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