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'''Parametric Programming''' denotes a type of [[mathematical programmingoptimization]], where the [[optimization problem]] is solved as a function of one or multiple [[parameters]].<ref>Tomas Gal. Postoptimal analyses, parametric programming, and related topics: Degeneracy, multicriteria decision making, redundancy. Berlin : W. de Gruyter, 1995.</ref> Developed in parallel to [[sensitivity analysis]], its earliest mention can be found in a master [[thesis]] from 1952.<ref>T Gal, H.J. Greenberg Advances in Sensitivity Analysis and Parametric Programming. Springer, 1997.</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 20022000 has contributed to an increased interest in the topic.<ref>Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N. (2000) The explicit solution of model predictive control via multiparametric quadratic programming. Proceedings of the American Control, vol. 2, 872-876.</ref><ref>Bemporad, Alberto; Morari, Manfred; Dua, Vivek; Pistikopoulos, Efstratios N. (2002) The explicit linear quadratic regulator for constrained systems. Automatica, 38 (1), 3-20.</ref>
== Notation ==
In general, the following optimization problem is considered
