JSEA  Vol.6 No.5 , May 2013
An Improved Line Search and Trust Region Algorithm
ABSTRACT
In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.

Cite this paper
Q. Zhou, Y. Zhang and X. Zhang, "An Improved Line Search and Trust Region Algorithm," Journal of Software Engineering and Applications, Vol. 6 No. 5, 2013, pp. 49-52. doi: 10.4236/jsea.2013.65B010.
References
[1]   J. J. Moré and D. C. Sorensen, “Computing a Trust Region Step,” SIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 3, 1983, pp. 553-572. doi:10.1137/0904038

[2]   M. J. D. Powell, “Convergence Properties of a Class of Minimization Algorithms,”O. L. Mangasarian, R. R. Meyer and S. M. Robinson eds. , Nonlinear Programming, Academic Press, New York, 1975, pp. 1-27.

[3]   R. Fletcher, “Practical Methods of Optimization, John Wiley and Sons,” New York, 1987.

[4]   A. R. Conn, N. I. M. Gould and Ph. L. Toint, “Trust-Region Methods,” SIAM, Philadelphia, 2000. doi:10.1137/1.9780898719857

[5]   G. X. Ma, “A Modified Trust Region Methods for Unconstrained Optimization (in Chinese),” Master's Thesis, 2003.

[6]   Q. H. Zhou, Y. R. Zhang, F. X. Xu and Y. Geng, “An Improved Trust Region Method for Unconstrained Optimization,” accepted by Science China Mathematics.

[7]   J. Nocedal and Y. Yuan, “Combining Trust Region and Line Search, Y. Yuan, ed.,” Advances in Nonlinear Programming, Kluwer, 1998, pp. 153-175.

[8]   J. J. Moré, B. S. Garbow and K. H. Hillstrom, “Testing Unconstrained Optimization Software,” ACM Transaction Mathematics, Vol. 7, No. 1, 1981, pp. 17-41.

 
 
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