Looking at some feasible sets from GRI-Mech dataset

2 Looking at some feasible sets from GRI-Mech dataset 

Other), adding just one more active variable into consideration resolves it by finding a mutually agreeable set of acceptable values. 

Accounting for more active variables expands the feasible set in additional dimensions. For example, expanding the dimensionality of the analysis to include an additional active variable, X34, pre-exponential factor of reaction 0H + CH3- CH2 + H20, reveals more. X34 is the second highest impact parameter for 55 and the fourth highest for 57. The three-dimensional feasible set is shown in Fig. 7. A cross-section of this feasible set by the plane X34 = 0 forms the darker shaded area in Fig. 6. With the addition of experiments and active variables, the geometry of the feasible set grows in complexity and is difficult to visualize. This necessitates developing theoretical and numerical methods to accurately account for known constraints (usually implied by data) in nonlinear and hybrid models. This is precisely the capability of the numerical methods described next. 

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