Encyclopedia of Law and Economics

2019 Edition
| Editors: Alain Marciano, Giovanni Battista Ramello

Optimization Problems

  • Roy CerquetiEmail author
  • Raffaella Coppier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7753-2_354


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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  1. Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & control: foundations & applications. Birkhäuser, BostonCrossRefGoogle Scholar
  2. Barro R, Sala-I-Martin X (2004) Economic growth, 2nd edn. The MIT PressGoogle Scholar
  3. 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):1–67CrossRefGoogle Scholar
  4. Fleming WH, Soner HM (2006) Controlled Markov processes and viscosity solutions, 2nd edn. Springer, New York/Heidelberg/BerlinGoogle Scholar
  5. Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, New York/Heidelberg/BerlinCrossRefGoogle Scholar
  6. 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, AmsterdamGoogle Scholar
  7. Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
  8. Mas-Colell A, Whinston M, Green J (1995) Microeconomic theory. Oxford University Press, OxfordGoogle Scholar
  9. Simon CP, Blume L (1994) Mathematics for economists. W.W. Norton & CompanyGoogle Scholar
  10. Varian H (1992) Microeconomic analysis, 3rd edn. W.W. Norton & CompanyGoogle Scholar
  11. Yong J, Zhou XY (1999) Stochastic controls. Springer, New York/Heidelberg/BerlinCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Economics and LawUniversity of MacerataMacerataItaly