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A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization

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Abstract

This paper mainly aims to study a new nonmonotone line search slackness technique for unconstrained optimization problems and show that it possesses the global convergence without needing condition of convexity. We establish the corresponding algorithm and illustrate its effectiveness by virtue of some numerical tests. Simulation results indicate that the proposed method is very effective for non-convex functions.

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References

  1. Ni, Q.: Optimization Methods and Programming. Science Press, Beijing (2009)

    Google Scholar 

  2. Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton’s methods. SIAM J. Numer. Anal. 23, 707–716 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Sun, W., Han, J., Sun, J.: Global convergence of non-monotone descent methods for unconstrained optimization problems. J. Comput. Appl. Math. 146, 89–98 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Yu, Z., Pu, D.: A new nonmonotone line search technique for unconstrained optimization. J. Comput. Appl. Math. 219, 134–144 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Grippo, L., Lampariello, F., Lucidi, S.: A truncated Newton method with nonmonotone line search for unconstrained optimization. J. Optim. Theory Appl. 60, 401–419 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  7. Shi, Z., Shen, J.: Convergence of PRP method with new nonmonotone line search. Appl. Math. Comput. 181, 423–431 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Shi, Z., Shen, J.: Convergence of nonmonotone line search method. J. Comput. Appl. Math. 193, 397–412 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun, W., Zhou, Q.: An unconstrained optimization method using nonmonotone second order Goldstein’s line search. Sci. China Ser. A 50, 1389–1400 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yu, Y., Gao, L.: Nonmonotone line search algorithm for constrained minimax problems. J. Optim. Theory Appl. 115, 419–446 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhou, Q., Sun, W.: Adaptive nonmonotone line search method for unconstrained optimization. Front. Math. China 3, 133–148 (2008)

    Article  MathSciNet  Google Scholar 

  12. Andrei, N.: An unconstrained optimizaition test functions collection. Adv. Model. Optim. 10, 147–161 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Shi, Z.J., Shen, J.: New inexact line search method for unconstrained optimization. J. Optim. Theory Appl. 127, 425–446 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Research supported by Grant HGA0905 and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.: 11KJB110001). The second author is partially supported by the National Natural Science Foundation of China (Grant No.: 51205151). The authors are very grateful to the referees for valuable comments and constructive suggestions which result in the present version of the article.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, China

    Ping Hu & Xu-Qing Liu

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  1. Ping Hu
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  2. Xu-Qing Liu
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Correspondence to Xu-Qing Liu.

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Communicated by Alexander S. Strekalovsky.

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Hu, P., Liu, XQ. A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization. J Optim Theory Appl 158, 773–786 (2013). https://doi.org/10.1007/s10957-012-0247-7

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  • DOI: https://doi.org/10.1007/s10957-012-0247-7

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