Annals of Operations Research

, Volume 62, Issue 1, pp 173–196 | Cite as

A relaxed primal-dual path-following algorithm for linear programming

  • Tsung-Min Hwang
  • Chih-Hung Lin
  • Wen-Wei Lin
  • Shu-Cherng Fang
Article
  • 92 Downloads

Abstract

In this paper, we provide an easily satisfied relaxation condition for the primaldual interior path-following algorithm to solve linear programming problems. It is shown that the relaxed algorithm preserves the property of polynomial-time convergence. The computational results obtained by implementing two versions of the relaxed algorithm with slight modifications clearly demonstrate the potential in reducing computational efforts.

Keywords

Linear programming primal-dual method interior path-following algorithm relaxation method 

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References

  1. [1]
    E.R. Barnes, A variation of Karmarkar's algorithm for solving linear programming problems, Math. Progr. 36(1986)174–182.Google Scholar
  2. [2]
    S.C. Fang and S.C. Puthenpura,Linear Optimization and Extensions: Theory and Algorithms (Prentice-Hall, Englewood Cliffs, NJ, 1993).Google Scholar
  3. [3]
    P.H. Gill, W. Murray, M.A. Saunders, J.A. Tomlin and M.H. Wright, On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method, Math. Progr. 36(1986)183–209.Google Scholar
  4. [4]
    D. Goldfarb and S. Mehrotra, A relaxed version of Karmarkar's method, Math. Progr. 40 (1988)289–315.Google Scholar
  5. [5]
    D. Goldfarb and S. Mehrotra, Relaxed variants of Karmarkar's algorithm for linear programs with unknown optimal objective value, Math. Progr. 40(1988)183–195.Google Scholar
  6. [6]
    D. Goldfarb and M.J. Todd, Linear programming, Technical Report No. 777, Cornell University, School of Operations Research and Industrial Engineering, Ithaca, New York (1988).Google Scholar
  7. [7]
    C.C. Gonzaga, An algorithm for solving linear programming problems inO(n 3 L) operations, in:Progress in Mathematical Programming: Interior-Point and Related Methods, ed. N. Megiddo (Springer, New York, 1989) pp. 1–28.Google Scholar
  8. [8]
    T.-M. Hwang, C.-H. Lin, W.-W. Lin and S.-C. Fang, Relaxing interior path following primaldual algorithm for linear programming, OR Report No. 270, North Carolina State University, Raleigh, NC (1993).Google Scholar
  9. [9]
    N. Karmarkar, A new polynomial time algorithm for linear programming, Combinatorica 4 (1984)373–395.Google Scholar
  10. [10]
    M. Kojima, S. Mizumo and A. Yoshise, A primal-dual interior point method for linear programming, in:Progress in Mathematical Programming: Interior-Point and Related Methods, ed. N. Megiddo (Springer, New York, 1989) pp. 29–48.Google Scholar
  11. [11]
    I.J. Lustig, R.E. Marsten and D.F. Shanno, Computational, experience with a primal-dual interior point method for linear programming, Linear Algebra and its Applications 152 (1991)191–222.Google Scholar
  12. [12]
    N. Megiddo, Pathways to the optimal set in linear programming, in:Progress in Mathematical Programming: Interior-Point and Related Methods, ed. N. Megiddo (Springer, New York, 1989) pp. 131–158.Google Scholar
  13. [13]
    N. Megiddo,Progress in Mathematical Programming: Interior-Point and Related Methods (Springer-Verlag, New York, 1989).Google Scholar
  14. [14]
    R.C. Monteiro and I. Adler, Interior path following primal-dual algorithms, Part I: Linear programming, Math. Progr. 44(1989)27–41.Google Scholar
  15. [15]
    R.C. Monteiro and I. Adler, Interior path following primal-dual algorithms, Part II: Convex quadratic programming, Math. Progr. 44 (1989)43–66.Google Scholar
  16. [16]
    R.J. Vanderbei, M.S. Meketon and B.A. Freeman, A modification of Karmarkar's linear programming algorithm, Algorithmica 1(1986)395–407.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Tsung-Min Hwang
    • 1
  • Chih-Hung Lin
    • 1
  • Wen-Wei Lin
    • 1
  • Shu-Cherng Fang
    • 2
  1. 1.Institute of Applied MathematicsNational Tsing Hua UniversityHsinchuTaiwan R.O.C.
  2. 2.Operations Research and Industrial EngineeringNorth Carolina State UniversityRaleighUSA

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