Convergence in Karmarkar's algorithm: a review

Abstract

A critical review is presented of works on convergence in Karmarkar's algorithm. Various inequalities, playing dominant roles in this regard are discussed. Finally, it is observed that on using fixed steplength (near α = l), convergence of iterates to optimal solution can be achieved in at most nq iterations and, on using optimal steplength at each iteration, faster convergence can be ensured.