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A New Technique for Estimating the Lower Bound of the Trust-Region Subproblem
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Abstract
Trust-region methods are popular for nonlinear optimization problems. How to determine the predicted reduction of the trust-region subproblem is a key issue for trust-region methods. Powell gave an estimation of the lower bound of the trust-region subproblem by considering the negative gradient direction. In this article, we give an alternate way to estimate the same lower bound of the trust-region subproblem.
KeywordsTrust-Region MethodUnconstrained OptimizationTrust-Region Subproblem
- J. E. Dennis and R. B. Schnabel, “Numerical Methods for Unconstrained Optimization and Nonlinear Equations,” Prentice-Hall, Inc., Englewood Cliffs, 1983.
- R. Fletcher, “Practical Methods of Optimization,” 2nd Edition, John Wiley & Sons, Chichester, 1987
- A. R. Conn, N. Gould and P. L. Toint, “Trust-Region Methods,” SIAM, Philadelphia, 2000. doi:10.1137/1.9780898719857
- J. Nocedal and S. J. Wright, “Numerical Optimization,” Springer-Verlag, New York, 1999. doi:10.1007/b98874
- M. J. D. Powell, “Convergence Properties of a Class of Minimization Algorithms,” In: O. L. Mangasarian, R. R. Meyer and S. M. Robinson Eds., Nonlinear Programming 2, Academic Press, New York, 1975, pp. 1-27.
- D. M. Gay, “Computing Optimal Locally Constrained Steps,” SIAM Journal on Scientific and Statistical Computing, Vol. 42, No. 2, 1981, pp. 186-197. doi:10.1137/0902016
- 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
- D. J. Higham, “Trust Region Algorithms and Time Step Selection,” SIAM Journal on Numerical Analysis, Vol. 37, No. 1, 1999, pp. 194-210. doi:10.1137/S0036142998335972
- X.-L. Luo, C. T. Kelley, L.-Z. Liao and H. W. Tam, “Combining Trust Region Techniques and Rosenbrock Methods to Compute Stationary Points,” Journal of Optimization Theory and Applications, Vol. 140, No. 2, 2009, pp. 265-286. doi:10.1007/s10957-008-9469-0
- X.-L. Luo, L.-Z. Liao and H. W. Tam, “Convergence Analysis of the Levenberg-Marquardt Method,” Optimization Methods and Software, Vol. 22, No. 4, 2007, pp. 659-678. doi:10.1080/10556780601079233
- X.-L. Luo, “A Second-Order Pseudo-Transient Method for Steady-State Problems,” Appllied Mathematics Computation, Vol. 216, No. 6, 2010, pp. 1752-1762. doi:10.1016/j.amc.2009.12.029