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Optimization Problems

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Abstract

This issue deals with the conceptualization of an optimization problem. In particular, we first provide a formal definition of such a mathematical concept. Then, we give some classifications of the optimization problems on the basis of their main characteristics (presence of time dependence and of constraints). In so doing, we also outline the standard techniques adopted for seeking solutions of an optimization problem. Lastly, some examples taken by the classical theory of economics and finance are proposed.

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References

  • Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & control: foundations & applications. Birkhäuser, Boston

    Book  Google Scholar 

  • Barro R, Sala-I-Martin X (2004) Economic growth, 2nd edn. The MIT Press

    Google Scholar 

  • Crandall MG, Ishii H, Lions P-L (1992) User's guide to viscosity solutions of second order partial differential equations. Bull Am Math Soc 27(1):1–67

    Article  Google Scholar 

  • Fleming WH, Soner HM (2006) Controlled Markov processes and viscosity solutions, 2nd edn. Springer, New York/Heidelberg/Berlin

    Google Scholar 

  • Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, New York/Heidelberg/Berlin

    Book  Google Scholar 

  • Kamien MI, Schwartz NL (1991) Dynamic optimization: the Calculus of variations and optimal control in economics and management, vol 31, 2nd edn, Advanced textbooks in economics. Elsevier B.V, Amsterdam

    Google Scholar 

  • Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91

    Google Scholar 

  • Mas-Colell A, Whinston M, Green J (1995) Microeconomic theory. Oxford University Press, Oxford

    Google Scholar 

  • Simon CP, Blume L (1994) Mathematics for economists. W.W. Norton & Company

    Google Scholar 

  • Varian H (1992) Microeconomic analysis, 3rd edn. W.W. Norton & Company

    Google Scholar 

  • Yong J, Zhou XY (1999) Stochastic controls. Springer, New York/Heidelberg/Berlin

    Book  Google Scholar 

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Correspondence to Roy Cerqueti .

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© 2016 Springer Science+Business Media New York

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Cerqueti, R., Coppier, R. (2016). Optimization Problems. In: Marciano, A., Ramello, G. (eds) Encyclopedia of Law and Economics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7883-6_354-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7883-6_354-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7883-6

  • eBook Packages: Springer Reference Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

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