Mest Linear vs Nonlinear 16888 E77 The objective function is a linear function of the design variables if each design variable appears only to the first power with constant coefficients multiplying it J(X)=X1+2x2-34X is linear in X=[x,X2 X3] J(x)=X1X2+2X2-34x3 is nonlinear in x J(x)=COS(X1)+2X2-3 4X3 is nonlinear in x 8 C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics8 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Linear vs. Nonlinear Linear vs. Nonlinear The objective function is a linear function of the design variables if each design variable appears only to the first power with constant coefficients multiplying it. 12 3 J xx x ( ) 2 3.4 x   is linear in x=[x1 x 2 x 3 ] T 12 2 3 J xx x x ( ) 2 3.4 x  is nonlinear in x 1 2 J xx ( ) cos( ) 2 3.4 x  3 x is nonlinear in x