Editing Mathematical optimization (section)

===Economics and finance===
[[Economics]] is closely enough linked to optimization of [[agent (economics)|agents]] that an influential definition relatedly describes economics ''qua'' science as the "study of human behavior as a relationship between ends and [[scarce]] means" with alternative uses.<ref>[[Lionel Robbins]] (1935, 2nd ed.) ''[[An Essay on the Nature and Significance of Economic Science#Major propositions|An Essay on the Nature and Significance of Economic Science]]'', Macmillan, p. 16.</ref> Modern optimization theory includes traditional optimization theory but also overlaps with [[game theory]] and the study of economic [[equilibrium (economics)|equilibria]]. The ''[[Journal of Economic Literature]]'' [[JEL classification codes|codes]] classify mathematical programming, optimization techniques, and related topics under [[JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories|JEL:C61-C63]].

In microeconomics, the [[utility maximization problem]] and its [[dual problem]], the [[expenditure minimization problem]], are economic optimization problems. Insofar as they behave consistently, [[consumer]]s are assumed to maximize their [[utility]], while [[firm]]s are usually assumed to maximize their [[Profit (economics)|profit]]. Also, agents are often modeled as being [[Risk aversion|risk-averse]], thereby preferring to avoid risk. [[Asset pricing|Asset prices]] are also modeled using optimization theory, though the underlying mathematics relies on optimizing [[stochastic process]]es rather than on static optimization. [[International trade theory]] also uses optimization to explain trade patterns between nations. The optimization of [[Portfolio (finance)|portfolios]] is an example of multi-objective optimization in economics.

Since the 1970s, economists have modeled dynamic decisions over time using [[control theory]].<ref>{{cite journal |first=Robert |last=Dorfman |author-link=Robert Dorfman |title=An Economic Interpretation of Optimal Control Theory |journal=[[American Economic Review]] |volume=59 |issue=5 |year=1969 |pages=817–831 |jstor=1810679 }}</ref> For example, dynamic [[search theory|search models]] are used to study [[labor economics|labor-market behavior]].<ref>{{cite book |first=Thomas J. |last=Sargent |author-link=Thomas J. Sargent |chapter=Search |title=Dynamic Macroeconomic Theory |publisher=Harvard University Press |year=1987 |pages=57–91 |isbn= 9780674043084|chapter-url=https://books.google.com/books?id=nVuyXF8ibeIC&pg=PA57 }}</ref> A crucial distinction is between deterministic and stochastic models.<ref>A.G. Malliaris (2008). "stochastic optimal control," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_S000269&edition=&field=keyword&q=Taylor's%20th&topicid=&result_number=1 Abstract] {{Webarchive|url=https://web.archive.org/web/20171018182459/http://www.dictionaryofeconomics.com/article?id=pde2008_S000269&edition=&field=keyword&q=Taylor's%20th&topicid=&result_number=1 |date=2017-10-18 }}.</ref> [[Macroeconomics|Macroeconomists]] build [[dynamic stochastic general equilibrium|dynamic stochastic general equilibrium (DSGE)]] models that describe the dynamics of the whole economy as the result of the interdependent optimizing decisions of workers, consumers, investors, and governments.<ref>{{cite journal |first1=Julio |last1=Rotemberg |author-link=Julio Rotemberg |author-link2=Michael Woodford (economist) |first2=Michael |last2=Woodford |year=1997 |title=An Optimization-based Econometric Framework for the Evaluation of Monetary Policy |journal=NBER Macroeconomics Annual |volume=12 |pages=297–346 |doi=10.2307/3585236 |jstor=3585236 |url=http://www.nber.org/chapters/c11041.pdf |doi-access=free }}</ref><ref>From ''[[The New Palgrave Dictionary of Economics]]'' (2008), 2nd Edition with Abstract links:<br />• "[http://www.dictionaryofeconomics.com/article?id=pde2008_N000148&edition=current&q=optimization&topicid=&result_number=1 numerical optimization methods in economics]" by Karl Schmedders<br />• "[http://www.dictionaryofeconomics.com/article?id=pde2008_C000348&edition=current&q=optimization&topicid=&result_number=4 convex programming]" by [[Lawrence E. Blume]]<br />• "[http://www.dictionaryofeconomics.com/article?id=pde2008_A000133&edition=current&q=optimization&topicid=&result_number=20 Arrow–Debreu model of general equilibrium]" by [[John Geanakoplos]].</ref>