论文信息 - Convergence of quasi-Newton method with new inexact line search☆

Convergence of quasi-Newton method with new inexact line search☆

Quasi-Newton method is a well-known effective method for solving optimization problems. Since it is a line search method, which needs a line search procedure after determining a search direction at each iteration, we must decide a line search rule to choose a step size along a search direction. In this paper, we propose a new inexact line search rule for quasi-Newton method and establish some global convergent results of this method. These results are useful in designing new quasi-Newton methods. Moreover, we analyze the convergence rate of quasi-Newton method with the new line search rule.

Zhen-Jun Shi | Zhenjun Shi

[1] A. Goldstein. On Steepest Descent , 1965 .

[2] L. Armijo. Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[3] M. N. Vrahatis,et al. A New Unconstrained Optimization Method for Imprecise Function and Gradient Values , 1996 .

[4] Houyuan Jiang,et al. Some Convergence Properties of Descent Methods , 1997 .

[5] P. Wolfe. Convergence Conditions for Ascent Methods. II: Some Corrections , 1971 .

[6] Stephen J. Wright,et al. Numerical Optimization , 2018, Fundamental Statistical Inference.

[7] P. Wolfe. Convergence Conditions for Ascent Methods. II , 1969 .

[8] M. Todd. On Convergence Properties of Algorithms for Unconstrained Minimization , 1989 .

[9] Elijah Polak,et al. Optimization: Algorithms and Consistent Approximations , 1997 .

[10] M. N. Vrahatis,et al. A class of gradient unconstrained minimization algorithms with adaptive stepsize - some corrections , 2000 .

[11] Zhen-Jun Shi,et al. Convergence of line search methods for unconstrained optimization , 2004, Appl. Math. Comput..