Table 2.

Results from the first parameter estimation using p-ARGONAUT. In this case, quadratic surrogates are fitted to the initial sampling points.

Unknown Equation	Surrogate Formulation from p-ARGONAUT
Objective	$f(x_1,x_2)=0.091-1.222x_1-0.038x_2+0.784x_1^2-2.254\cdot {10}^{-7}{x}_1{x}_2+0.276x_2^2$
Constraint #1	$1.478-1.385x_1-0.795x_2+0.621x_1^2-3.550\cdot {10}^{-8}{x}_1{x}_2+0.219x_2^2\le 0$
Constraint #2	$1.029-1.675x_1-0.037x_2+0.751x_1^2-8.010\cdot {10}^{-8}{x}_1{x}_2+0.265x_2^2\le 0$
Constraint #3	$0.325-1.098x_1-0.218x_2-0.316x_1^2-1.117\cdot {10}^{-7}{x}_1{x}_2-0.111x_2^2\le 0$