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A Hybrid Descent Method for Global Optimization

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Abstract

In this paper, a hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm is used to locate descent points for previously converged local minima. The combined method has the descent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed hybrid descent method, several multi-dimensional non-convex optimization problems are solved. Numerical examples show that global minimum can be sought via this hybrid descent method.

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References

  1. Bagirov, A. and Rubinov, A. (2003), Cutting angle method and a local search. Journal of Global Optimization 27, 193–213.

    Google Scholar 

  2. Barhen, J., Protopopescu, V. and Reister, D. (1997), TRUST: A deterministic algorithm for global optimization, Science, 276, 1094–1097.

    Google Scholar 

  3. Cerny, V. (1985), Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm, Journal of Optimization Theory and Applications 45, 41–51.

    Google Scholar 

  4. Cetin, B., Barhen, J. and Burdick, J. (1993), Terminal repeller unconstarined subenergy tunneling (TRUST) for fast global optimization, Journal of Optimization and Applications 77, 97–126.

    Google Scholar 

  5. Ge, R. (1987), The theory of filled function method for finding global minimizers of nonlinearly constrained minimization problems, Journal of Computational Mathematics 5(1), 1–9.

    Google Scholar 

  6. Ge, R. (1990), A filled function method for finding a global minimizer of a function of several variables, Mathematical Programming 46, 191–204.

    Google Scholar 

  7. Ge, R. and Qin, Y. (1987), A class of filled functions for finding global minimizers of a function of several variables, Journal of Optimization Theory and Applications 52(2), 240–252.

    Google Scholar 

  8. Griewank, A. (1981), Generalized descent for global optimization, Journal of Optimization Theory and Applications 34, 11–39.

    Google Scholar 

  9. Kirkpatrick, S. Jr., C. D. G. and Vecchi, M. P. (1983), Optimization by simulated annealing, Science, 220: 671–680.

    Google Scholar 

  10. Levy, A. and Montalvo, A. (1985), The tunneling algorithm for the global minimization of functions, SIAM Journal of Scientific and Statistical Computing 6, 15–29.

    Google Scholar 

  11. Liu, X. (2001), Finding global minima with a computable filled function, Journal of Global Optimization, 19, 151–161.

    Google Scholar 

  12. Liu, Y. and Teo, K. (1999), A bridging method for global optimization, Journal of Australian Mathematical Society Series B 41, 41–57.

    Google Scholar 

  13. Locatelli, M. (2000), Simulated annealing algorithms for continuous global optimization: convergence conditions, Journal of Optimization Theory and Applications, 104(1), 121–133.

    Google Scholar 

  14. Ng, C. and Li, D. (2001), A sequential constrained minimization method for constrained global optimization. In: Proceedings of the 5th International Conference on Optimization: Techniques and Applications, Hong Kong, pp. 990–997.

  15. Pardalos, P., Ye, Y. and Han, C. (1991), Algorithms for the solution of quadratic knapsack problems, Linear Algebra and its Applications 152, 69–91.

    Google Scholar 

  16. Press, W., Teukolsky, S., Vetterling, W. and Flannery, B. (1992), Numerical Recipes in Fortran: the art of scientific computing (2nd Ed.). Cambridge University Press, Cambridge.

    Google Scholar 

  17. Rubinov, A. (2000), Abstract Convexity and Global Optimization. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  18. Shubert, B. (1972), A sequential method seeking the global maximum of a function, SIAM Journal of Numerical Analysis, 9, 379–388.

    Google Scholar 

  19. Xu, Z., Huang, H., Pardalos, P. and Xu, C. (2001), Filled functions for unconstrained global optimization, Journal of Global Optimization, 20, 49–65.

    Google Scholar 

  20. Yao, Y. (1989), Dynamic tunneling algorithm for global optimization, IEEE Transactions on Systems, Man, and Cybernetics 19, 1222–1230.

    Google Scholar 

  21. Zhang, L., Ng, C., Li, D. and Tian, W. (2001), A new filled function method for global optimization, Journal of Global Optimization, to appear.

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Authors and Affiliations

  1. Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

    Y. Liu & K.L. Teo

  2. Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong

    K.F.C. Yiu

Authors
  1. K.F.C. Yiu
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  2. Y. Liu
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  3. K.L. Teo
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Yiu, K., Liu, Y. & Teo, K. A Hybrid Descent Method for Global Optimization. Journal of Global Optimization 28, 229–238 (2004). https://doi.org/10.1023/B:JOGO.0000015313.93974.b0

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  • DOI: https://doi.org/10.1023/B:JOGO.0000015313.93974.b0

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