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.
This is a preview of subscription content, log in via an institution.
References
Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & control: foundations & applications. Birkhäuser, Boston
Barro R, Sala-I-Martin X (2004) Economic growth, 2nd edn. The MIT Press
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
Fleming WH, Soner HM (2006) Controlled Markov processes and viscosity solutions, 2nd edn. Springer, New York/Heidelberg/Berlin
Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, New York/Heidelberg/Berlin
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
Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91
Mas-Colell A, Whinston M, Green J (1995) Microeconomic theory. Oxford University Press, Oxford
Simon CP, Blume L (1994) Mathematics for economists. W.W. Norton & Company
Varian H (1992) Microeconomic analysis, 3rd edn. W.W. Norton & Company
Yong J, Zhou XY (1999) Stochastic controls. Springer, New York/Heidelberg/Berlin
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
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
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7883-6_354-1
Received:
Accepted:
Published:
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