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An integral function and vector sequence method for unconstrained global optimization

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Abstract

An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm.

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References

  1. Bazaraa M.S., Sherali H.D., Shetty C.M.: Nonlinear Programming. 2nd edn. Wiley, New York (1993)

    Google Scholar 

  2. Cetin B.C., Barhen J., Burdick J.W.: Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization. J.O.T.A. 77(1), 97–125 (1993)

    Article  Google Scholar 

  3. Floudas C.A., Pardalos P.M., Adjiman C.S., Esposito W.R., Gumus Z.H., Harding S.T., Klepeis J.L., Meyer C.A., Schweiger C.A.: Handbook of Test Problems in Local and Global Optimization. Kluwer, Dordrecht, The Netherlands (1999)

    Google Scholar 

  4. Ge R.P.: A filled function method for finding a global minimzer of a function of several variables. Math. Program. 46, 191–204 (1990)

    Article  Google Scholar 

  5. Ge R.P., Qin Y.F.: The globally convexized filled functions for global optimization. Appl. Math. Comput. 35, 131–158 (1990)

    Article  Google Scholar 

  6. Global Optimization Laboratory web site, http://globopt.dsi.unifi.it/gol/TestFunctions1.0/index.html (2006)

  7. Han Q.M., Han J.: Revised filled function methods for global optimization. Appl. Math. Comput. 119, 217–228 (2001)

    Article  Google Scholar 

  8. Horst R., Tuy H.: Global Optimization: Deterministic Approaches. 2nd edn. Springer, Heidelberg (1993)

    Google Scholar 

  9. Horst R., Pardalos M.P., Thoai N.V.: Introduction to Global Optimization. Kluwer, Dordrecht, Netherlands (1995)

    Google Scholar 

  10. Levy A.V., Montalvo A.: The tunneling algorithm for the global minimization of functions. SIAM J. Sci. Stat. Comput. 6(1), 15–29 (1985)

    Article  Google Scholar 

  11. Locatelli M.: A note on the griewank test function. J. Glob. Optim. 25, 169–174 (2003)

    Article  Google Scholar 

  12. Lucidi S., Piccialli V.: New classes of globally convexized filled functions for global optimization. J. Glob. Optim. 24, 219–236 (2002)

    Article  Google Scholar 

  13. Pardalos P., Romeijn H.E.: Handbook of Global Optimization. Kluwer, Dordrecht, Netherlands (2002)

    Google Scholar 

  14. Pardalos P.M., Rosen J.B.: Constrained Global Optimization: Algorithms and Applications. Springer, Berlin (1987)

    Book  Google Scholar 

  15. Törn A., Zilinskas A.: Global Optimization. Springer, Berlin (1989)

    Google Scholar 

  16. Yao Y.: Dynamic tunneling algorithm for global optimization. IEEE Trans. Syst. Man Cybern. 19(5), 1222–1230 (1989)

    Article  Google Scholar 

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Author notes

  1. Fusheng Bai

    Present address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, VC, 3353, Australia

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, 200444, Shanghai, China

    Yongjian Yang

  2. School of Mathematics and Computer Science, Chongqing Normal University, 400047, Chongqing, China

    Fusheng Bai

Authors
  1. Yongjian Yang
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  2. Fusheng Bai
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Corresponding author

Correspondence to Yongjian Yang.

Additional information

This work was supported by the National Natural Science Foundation (No. 10571116).

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Yang, Y., Bai, F. An integral function and vector sequence method for unconstrained global optimization. J Glob Optim 50, 293–311 (2011). https://doi.org/10.1007/s10898-010-9581-1

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  • DOI: https://doi.org/10.1007/s10898-010-9581-1

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