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'''Parametric programming''' is a type of [[mathematical optimization]], where the [[optimization problem]] is solved as a function of one or multiple [[parameters]].<ref>{{cite book |last1=Gal |first1=Tomas |year=1995 |title=Postoptimal Analyses, Parametric Programming, and Related Topics: Degeneracy, Multicriteria Decision Making, Redundancy |publisher=W. de Gruyter |___location=Berlin |isbn=978-3-11-087120-3 |edition=2nd}}</ref> Developed in parallel to [[sensitivity analysis]], its earliest mention can be found in a [[thesis]] from 1952.<ref>{{cite book |last1=Gal |first1=Tomas |last2=Greenberg |first2=Harvey J. |date=1997 |title=Advances in Sensitivity Analysis and Parametric Programming |publisher=Kluwer Academic Publishers |___location=Boston |doi=10.1007/978-1-4615-6103-3 |isbn=978-0-7923-9917-9 |series=International Series in Operations Research & Management Science |volume=6}}</ref> Since then, there have been considerable developments for the cases of multiple parameters, presence of [[integer]] variables as well as nonlinearities. In particular the connection between parametric programming and [[model predictive control]] established in 2000 has contributed to an increased interest in the topic.<ref>{{cite book |last1=Bemporad |first1=
== Notation ==
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* If more than one parameter is present, i.e. <math>m > 1</math>, then it is often referred to as multiparametric programming problem<ref>{{cite journal|last1=Gal|first1=Tomas|last2=Nedoma|first2=Josef|title=Multiparametric Linear Programming|journal=Management Science|date=1972|volume=18|issue=7|pages=406–422|jstor=2629358}}</ref>
* If integer variables are present, then the problem is referred to as (multi)parametric mixed-integer programming problem<ref>{{cite journal|last1=Dua|first1=Vivek|last2=Pistikopoulos|first2=Efstratios N.|title=Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems|journal=Industrial & Engineering Chemistry Research|date=October 1999|volume=38|issue=10|pages=3976–3987|doi=10.1021/ie980792u}}</ref>
* If constraints are [[Affine transformation|affine]], then additional classifications depending to nature of the objective function in (multi)parametric (mixed-integer) linear, quadratic and nonlinear programming problems is performed. Note that this generally assumes the constraints to be affine.<ref>{{cite book|last1=Pistikopoulos |first1=
==References==
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