Skip to main content
SpringerLink
Log in

Convergence analysis of a nonlinear Lagrangian algorithm for nonlinear programming with inequality constraints

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we establish a nonlinear Lagrangian algorithm for nonlinear programming problems with inequality constraints. Under some assumptions, it is proved that the sequence of points, generated by solving an unconstrained programming, convergents locally to a Kuhn-Tucker point of the primal nonlinear programming problem.

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. D. P. Bertseks,Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.

    Google Scholar 

  2. D. P. Bertseks,Nonlinear Programming: Second Edition, Athena Scientific, Belmont, Massachusetts, 1999.

    Google Scholar 

  3. A. S. El-bakry, R. A. Tapia, T. Tsuchiya and Y. Zhang,On the fomulation and theory of the Newton interior-point method for nonlinear programming, Jornal of the Optimization Theory and Applications,89 (1996), 507–541.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. A. Polyak,Modified barrier functions (theory and methods), Mathematical programming,54 (1992), 177–222.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Yable and H. Yamashita,Q-superlinear convergence of primal-dual interior point quasi-Newton methods for constrained optimizition, Joural of the Operation Research Society of Japan,40 (1997), 415–436.

    Google Scholar 

  6. H. Yamashita,A globally convergent primal-dual interior point method for constrained optimization, Technical Report, Mathatical Systems Insitute, Inc., Tokyo, Japan, 1992.

    Google Scholar 

  7. H. Yamashita and H. Yable,Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization, Math. Programming,75 (1996), 377–397.

    MathSciNet  Google Scholar 

  8. L.-W. Zhang and S.-X. He,The convergence of a dual algorithm for nonlinear programming, Korean. J. Comput. & Appl. Math., Vol.7 (2000), No.3, 478–506.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, 116024, Dalian, China

    Li-Wei Zhang & Yong-Jin Liu

Authors
  1. Li-Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong-Jin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Youth NSF of China under project grant NO. 10001007.

Li-Wei Zhang received his Master Degree and PH.D from Dalian University of Technology. He has been at Dalian University of Technology since 1989. In 1999, he was made professor at the age of 35. His research interests focus on the algorithm for nonlinear programming, ABS algorithm and nonsmooth optimization. Also he studies mixed-integer programming and semi-definite programming.

Yong-Jin Liu is a PH.D candidate of Dalian University of Technology under the direction of Prof. Li-Wei Zhang. He is concerned with the algorithm for nonlinear programming and semi-definite programming.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, LW., Liu, YJ. Convergence analysis of a nonlinear Lagrangian algorithm for nonlinear programming with inequality constraints. JAMC 13, 1–10 (2003). https://doi.org/10.1007/BF02936070

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02936070

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation