Parametric programming: Difference between revisions

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Depending on the nature of <math>f(x,\theta)</math> and <math>g(x,\theta)</math> and whether the optimization problem features integer variables, parametric programming problems are classified into different sub-classes:

* If more than one parameter is present, i.e. <math>m > 1</math>, then it is often referred to as multiparametric programming problem<ref>Gal, Tomas; Nedoma, Josef (1972) Multiparametric Linear Programming. Management Science, 18 (7), 406-422.</ref>

* If integer variables are present, then the problem is referred to as (multi)parametric mixed-integer programming problem<ref>Dua, Vivek; Pistikopoulos, Efstratios N. (1999) Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems. Industrial & Engineering Chemistry Research, 38 (10), 3976-3987.</ref>

* If constraints are linear[[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>Pistikopoulos, Efstratios N.; Georgiadis, Michael C.; Dua, Vivek Multi-parametric programming: Theory, algorithms and applications. Weinheim, Wiley-VCH, 2007.</ref>

==References==