A Note on Karmarkar's Projective Transformation

This note corrects a certain inaccuracy in the discussion of the projective transformation employed by Karmarkar in the reduction of a general linear programming to the form required for his algorithm In his famous paper Karmarkar proposes on page Step a reduction of a general problem to one on a subset of the unit simplex as follows Given a linear programming problemof the form Minimize cx subject to Ax b x where an optimal solution is assumed to exist and the optimal value is assumed to be zero and a point a such that Aa b de ne a transformation x y T x by yi xi ai P j xj aj i n