esd Sequential Linear Programming 16888 Consider a general nonlinear problem linearized via first order Taylor series min√(x)≈√(x0)+VJ(x)yδx stg(x)≈g(x)+Vg(x)x≤0 h(x)≈h(x)+Vh2(x)x=0 X≤x1+x1≤x Where Sx=X-X This is an lp problem with the design variables contained in sx. the functions and gradients evaluated at X are constant coefficients o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics10 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Sequential Linear Programming Sequential Linear Programming Consider a general nonlinear problem linearized via first order Taylor series: 0 0 0 0 0 0 mi n ( ) ( ) ( ) s.t. ( ) ( ) ( ) 0 ( ) ( ) ( ) 0 T T j j j T k k k u i i i i J J J g g g h h h x x x x δ δ δ δ ≈ + ∇ ≈ + ∇ ≤ ≈ + ∇ = ≤ + ≤ x x x x x x x x x x x x A 0 where δ x x = − x This is an LP problem with the design variables contained in δ x. The functions and gradients evaluated at x 0 are constant coefficients