GLOBAL CONVERGENCE OF THE AFFINE SCALING ALGORITHM FOR CONVEX QUADRATIC-PROGRAMMING

In this paper we give a global convergence proof of the second-order a ffine scaling algorithm for convex quadratic programming problems, whe re the new iterate is the point which minimizes the objective function over the intersection of the feasible region with the ellipsoid cente red at the current point and whose radius is a fixed fraction beta is an element of (0; 1] of the radius of the largest ''scaled'' ellipsoid inscribed in the nonnegative orthant. The analysis is based on the lo cal Karmarkar potential function introduced by Tsuchiya. For any beta is an element of (0; 1) and without assuming any nondegeneracy assumpt ion on the problem, it is shown that the sequences of primal iterates and dual estimates converge to optimal solutions of the quadratic prog ram and its dual, respectively.