MODIFIED PREDICTOR-CORRECTOR ALGORITHM FOR LOCATING WEIGHTED CENTERS IN LINEAR-PROGRAMMING

In certain applications of linear programming, the determination of a particular solution, the weighted center of the solution set, is often desired, giving rise to the need for algorithms capable of locating s uch center. In this paper, we modify the Mizuno-Todd-Ye predictor-corr ector algorithm so that the modified algorithm is guaranteed to conver ge to the weighted center for given weights. The key idea is to ensure that iterates remain in a sequence of shrinking neighborhoods of the weighted central path. The modified algorithm also possesses polynomia lity and superlinear convergence.