A relaxed version of Karmarkar's algorithm is developed that does not require the direction of movement to be in the null space of the constraint matrix. The algorithm is proved to have the same rate of convergence as Karmarkar's algorithm. Conditions are also given guaranteeing that the approach suggested by Karmarkar for transforming an "inequality form" linear program into the form required by his algorithm is well defined.
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Aug 1989|