NARENDRA  KARMARKAR

Karmarkar’s Famous algorithm

                           Karmarkar’s algorithm solves the various linear Programming problems in the polynomial time. These problems are mostly represented by a “n” variables and a “m” constraints. The previous used method for solving these type of problems consisted a lot of problem representation by a “x” sided solid with a “y” vertices, where all the solution was then approached by traversing it from the vertex tovertex. Karmarkar’s novel method approaches all the solution by method of cutting through the all the above solid in all its traversal.        

                      Consequently, the complex optimization problems are also solved much faster using the method of Karmarkar algorithm. A practical example of this type of efficiency is the solution to a very complex problem in the communications network optimization where all the solution time taken was reduced from the weeks to some days. His algorithm thus enables the faster business and various policy decisions. Karmarkar’s algorithm has also stimulated all the development of the several other used interior point methods, some of which are now used in the current codes for solving the linear programs.