Abstract
This note focuses on developing quasi-Newton methods
that combine
This note focuses on developing quasi-Newton methods
that combine
D. Goldfarb, “A family of variable-metric methods derived by variational means,” Mathematics of Computation, vol. 24, pp. 23–26, 1970.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Mathematics of Computation, vol. 24, pp. 647–656, 1970.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. F. Shanno and K. H. Phua, “Matrix conditioning and nonlinear optimization,” Mathematical Programming, vol. 14, no. 2, pp. 149–160, 1978.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Ford and R.-A. Ghandhari, “On the use of function-values in unconstrained optimisation,” Journal of Computational and Applied Mathematics, vol. 28, pp. 187–198, 1989.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Ford and I. A. R. Moghrabi, “Alternative parameter choices for multi-step quasi-Newton methods,” Optimization Methods and Software, vol. 2, pp. 357–370, 1993.
View at: Google ScholarD. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming, vol. 45, no. 3, pp. 503–528, 1989.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. El-Baali, “Extra updates for the BFGS method,” Optimization Methods and Software, vol. 9, no. 2, pp. 1–21, 1999.
View at: Google ScholarR. H. Byrd, R. B. Schnabel, and G. A. Shultz, “Parallel quasi-Newton methods for unconstrained optimization,” Mathematical Programming, vol. 42, no. 2, pp. 273–306, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. H. Byrd and J. Nocedal, “A tool for the analysis of quasi-Newton methods with application to unconstrained minimization,” SIAM Journal on Numerical Analysis, vol. 26, no. 3, pp. 727–739, 1989.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Ford and I. A. R. Moghrabi, “Multi-step quasi-Newton methods for optimization,” Journal of Computational and Applied Mathematics, vol. 50, no. 1–3, pp. 305–323, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Ford and A. F. Saadallah, “A rational function model for unconstrained optimization,” in Numerical Methods (Miskolc, 1986), vol. 50 of Colloquia Mathematica Societatis János Bolyai, pp. 539–563, North-Holland, Amsterdam, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNet