Skip to main content
SpringerLink
Log in

An infeasible interior-point algorithm with full-Newton step for linear optimization

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

Recently, Roos (SIAM J Optim 16(4):1110–1136, 2006) presented a primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. In the current paper we use a different feasibility step such that the definition of the feasibility step in Mansouri and Roos (Optim Methods Softw 22(3):519–530, 2007) is a special case of our definition, and show that the same result on the order of iteration complexity can be obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Achache, M.: A new primal-dual path-following method for convex quadratic programming. Comput. Appl. Math. 25(1), 97–110 (2006)

    Article  MathSciNet  Google Scholar 

  2. Mansouri, H., Roos, C.: Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton step. Optim. Methods Softw. 22(3), 519–530 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mizuno, S.: Polynomiality of infeasible-interior-point algorithms for linear programming. Math. Program. 67(1), 109-119 (1994)

    Article  MathSciNet  Google Scholar 

  4. Peng, J., Roos, C., Terlaky, T.: New complexity analysis of the primal-dual Newton method for linear optimization. Ann. Oper. Res. 99(1), 23–39 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Peng, J., Roos, C., Terlaky, T.: A new class of polynomial primal-dual methods for linear and semidefinite optimization. Eur. J. Oper. Res. 143(2), 234–256 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press, Princeton (2002)

    MATH  Google Scholar 

  7. Potra, F.A.: An infeasible interior-point predictor-corrector algorithm for linear programming. SIAM J. Optim. 6(1), 19–32 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Roos, C.: A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 16(4), 1110–1136 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Roos, C., Terlaky, T., Vial, J.-Ph.: Theory and Algorithms for Linear Optimization. An Interior Approach. Wiley, Chichester (1997)

    MATH  Google Scholar 

  10. Salahi, M., Terlaky, T., Zhang, G.: The complexity of self-regular proximity based infeasible IPMs. Comput. Optim. Appl. 33(2), 157–185 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sun, W., Yuan, Y.: Optimization Theory and Methods: Nonlinear Programming. Springer, New York (2006)

    MATH  Google Scholar 

  12. Todd, M.J., Ye, Y.: A lower bound on the number of iterations of long-step and polynomial interior-point linear programming algorithms. Ann. Oper. Res. 62(1), 233–252 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ye, Y.: Interior Point Algorithms: Theory and Analysis. Wiley, New York (1997)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China

    Zhongyi Liu & Wenyu Sun

  2. College of Science, Hohai University, Nanjing, 210098, China

    Zhongyi Liu

Authors
  1. Zhongyi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenyu Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenyu Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Z., Sun, W. An infeasible interior-point algorithm with full-Newton step for linear optimization. Numer Algor 46, 173–188 (2007). https://doi.org/10.1007/s11075-007-9135-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-007-9135-x

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation