Linear Programming 16888 Most engineering problems of interest are nonlinear Can often simplify nonlinear problem by linearization LP is often the basis for developing more complicated NLP algorithms Standard LP problem min√(x)=∑cX minJ(x)=c′x Ax=b ∑aX=bj=1…m X≥0 X≥0=1.…,n All LP problems can be converted to this form o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics7 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Linear Programming Linear Programming Most engineering problems of interest are nonlinear • Can often simplify nonlinear problem by linearization • LP is often the basis for developing more complicated NLP algorithms Standard LP problem: All LP problems can be converted to this form. = = = = = ≥ = ∑ ∑ 1 1 mi n ( ) 1,.., 0 1,..., n i i i n ij i j i i J c x a x b j m x i n x min ( ) 0 1,..., T i J x i n = = ≥ = x c x Ax b