Journal of Optimization Theory and Applications

, Volume 80, Issue 2, pp 319–331 | Cite as

Modified predictor-corrector algorithm for locating weighted centers in linear programming

  • Y. Zhang
  • A. El-Bakry
Contributed Papers


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 such center. In this paper, we modify the Mizuno-Todd-Ye predictor-corrector algorithm so that the modified algorithm is guaranteed to converge 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 polynomiality and superlinear convergence.

Key Words

Predictor-corrector algorithm weighted center of the solution set linear programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Charnes, A., Cooper, W. W., andThrall, R. M.,A Structure for Classifying and Characterizing Efficiency and Inefficiency in Data Envelopment Analysis, Journal of Productivity Analysis, Vol. 2, pp. 197–237, 1991.CrossRefGoogle Scholar
  2. 2.
    Thrall, R. M., Private Communications, 1991.Google Scholar
  3. 3.
    Gonzaga, C. C.,Path-Following Methods for Linear Programming, SIAM Review, Vol. 34, pp. 167–224, 1992.CrossRefGoogle Scholar
  4. 4.
    McLinden, L.,An Analogue of Moreau's Proximation Theorem, with Application to the Nonlinear Complementarity Problem, Pacifi Journal of Mathematics, Vol. 88, pp. 101–161, 1980.Google Scholar
  5. 5.
    Megiddo, N.,Pathways to the Optimal Set of Linear Programming, Progress in Mathematical Programming, Interior-Point, and Related Methods, Edited by N. Megiddo, Springer-Verlag, New York, New York, pp. 131–158, 1989.Google Scholar
  6. 6.
    Mizuno, S., Todd, M. J., andYe, Y.,On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming, Technical Report No. 944, School of OR/IE, Cornell University, 1990.Google Scholar
  7. 7.
    Ye, Y., Güler, O., Tapia, R. A., andZhang, Y., Quadratically Convergent\(O(\sqrt {nL} )\) Algorithm for Linear Programming, Technical Report TR91-26, Department of Mathematical Sciences, Rice University, 1991.Google Scholar
  8. 8.
    Zhang, Y., andTapia, R. A.,On the Convergence of Interior-Point Methods to the Center of Solution Set in Linear Programming, Technical Report TR91-30, Department of Mathematical Sciences, Rice University, 1991.Google Scholar
  9. 9.
    Hoffman, A. J.,On Approximate Solutions of Systems of Linear Inequalities, Journal of Research of the National Bureau of Standards, Vol. 49, pp. 263–265, 1952.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Y. Zhang
    • 1
  • A. El-Bakry
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimoreMaryland
  2. 2.Department of Mathematical Sciences and Center for Research in Parallel ComputationRice UniversityHouston

Personalised recommendations