Skip to main content
SpringerLink
Log in

On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient.

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. W.I. Zangwill, “Nonlinear programming via penalty function,” Manangement Science, vol. 13, pp. 334–358, 1967.

    Google Scholar 

  2. S.P. Han and O.L. Mangasrian, “Exact penalty function in nonlinear programming,” Mathematical Programming, vol. 17, pp. 251–269, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Rosenberg, “Globally convergent algorithms for convex programming,” Mathematics of Operational Rresearch, vol. 6, pp. 437–443, 1981.

    Article  MATH  Google Scholar 

  4. J.B. Lasserre, “A globally convergent algorithm for exact penalty functions,” European Journal of Opterational Research, vol. 7, pp. 389–395, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  5. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1982.

    Google Scholar 

  6. E. Rosenberg, “Exact penalty functions and stability in locally Lipschitz programming,” Mathematical Programming, vol. 30, pp. 340–356, 1984.

    MATH  MathSciNet  Google Scholar 

  7. G. Di Pillo and L. Grippo, “An exact penalty function method with global conergence properties for nonlinear programming problems,” Mathemathical Programming, vol. 36, pp. 1–18, 1986.

    MathSciNet  Google Scholar 

  8. G. Di Pillo and L. Grippo, “On the exactness of a class of nondifferentiable penalty function,” Journal of Optimization Theory and Applications, vol. 57, pp. 385–406, 1988.

    Article  MathSciNet  Google Scholar 

  9. S.A. Zenios, M.C. Pinar, and R.S. Dembo, “A smooth penalty function algorithm for network-structured problems,” European Journal of Operational Research, vol. 64, pp. 258–277, 1993.

    Article  Google Scholar 

  10. M.C. Pinar and S.A. Zenios, “On smoothing exact penalty functions for convex constarained optimization,” SIAM Journal on Optimization, vol. 4, pp. 486–511, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  11. C. Chen and O.L. Mangasarian, “Smoothing methods for convex inequalities and linear complementarity problems,” Mathematical Programming, vol. 71, pp. 51–69, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  12. X.Q. Yang, Z.Q. Meng, X.X. Huang, and G.T.Y. Pong, “Smoothing nonlinear penalty functions for constrained optimization,” Numerical Functional Analysis and Optimization, vol. 24, pp. 351–364, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  13. S.C. Fang, J.R. Rajasekera, and H.S.J. Tsao, Entropy Optimization and Mathematical Proggramming, Kluwer, 1997.

  14. L. Qi, S.Y. Wu, and G. Zhou, “Semismooth newton methods for solving semi-infinite programming problems,” Journal of Global Optimization, vol. 27, pp. 215–232, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  15. K.L. Teo, X.Q. Yang, and L.S. Jennings, “Computational discretization algorithms for functional inequality constrained optimization,” Annals of Operations Research, vol. 98, pp. 215–234, 2000.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Business and Administration, Zhejiang University of Technology, Hangzhou, Zhejiang, 310032, China

    Zhiqing Meng

  2. Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong

    Chuangyin Dang

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Xiaoqi Yang

Authors
  1. Zhiqing Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuangyin Dang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoqi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiqing Meng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meng, Z., Dang, C. & Yang, X. On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization. Comput Optim Applic 35, 375–398 (2006). https://doi.org/10.1007/s10589-006-8720-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-006-8720-6

Keywords

Search

Navigation