Weighted Integral Objective Function

Previously, for multipoint optimization problems, we defined the objective function as the sum of drag coefficients at on-design points. We are now using a weighted integral to define an objective function for a multipoint optimization problem. The weighted integral represents the average drag over a range of Mach numbers and lift coefficients. A 'designer-priority' weighting function given by D allows the user to prioritize the range of Mach numbers and lift coefficients according to mission requirements. The trapezoidal quadrature rule is used to approximate the weighted integral. The objective function is defined as the approximation of the weighted integral given by:

$\mathcal{J} = \sum_{i=1}^{N_M}\sum_{j=1}^{N_{Cl}}\omega_{i,j}C_d\left(M_i,C_{l_{j}}\right) \simeq \int\limits_{C_{l1}}^{C_{l2}}\int\limits_{M_{1}}^{M_{2}} C_d\left(M,C_l\right)\mathcal{D}\left(M,C_l\right)\hspace{0.01in}dMdC_{l}$