Hybridization rule applied on accelerated double step size optimization scheme

Abstract

A hybrid accelerated model with two step length parameters for solving unconstrained optimization problems is presented. Applied hybridization process involves an efficient three term hybrid method. The accelerated double step size model is taken as guiding operator in this hybridization process. Defined method is convergent on the set of uniformly convex functions as well as on the set on strictly convex quadratics. We display a Dolan Moré performance profiles of derived iteration and of some other comparative hybrid and accelerated methods regarding the number of iterations and the number of function evaluations metrics. Displayed numerical test results confirm that derived model keeps a good properties of its forerunner method and outperform other comparative hybrid accelerated schemes.

A new three-term conjugate gradient method for solving the finite minimax problems

“…There are many well-known conjugate gradient methods, such as [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][34][35][36][37][38][39][40][41][42]. In [12], the iterative formula of three-term conjugate gradient method is…”

“…For three-term conjugate gradient methods [12][13][14][15][16][17][18][19][20][21][22] and the related methods [23][24][25][26] posse low memory requirement and simple implementation, conjugate gradient methods are often used for solving unconstrained optimization problems. Recently, many researchers have presented kinds of three-term conjugate gradient method for solving the unconstrained optimization problems.Hence, we consider using three-term conjugate gradient method to solve the finite minimax problems.…”

On the Hybridization of the Double Step Length Method for Solving System of Nonlinear Equations

“…where T : Ω −→ Ω is a mapping defined on nonempty convex subset Ω of a normed space E, a k and v k are sequences determined by the iteration (16), and {η k } is the sequence of positive numbers in (0, 1). Following that, in [14], the hybridization rule in [17] is applied to the double step length scheme in order to improve the convergence properties of the double step length method in [13].…”

“…Based on the literature reviewed above, it can be concluded that using the hybridization process is an excellent way to improve the convergence properties and numerical experiments of some existing methods. Therefore, motivated by the idea presented by Petrović in [14] and the approximation in (14), this paper aims to develop a hybrid double direction and step length method for solving a system of nonlinear equations via…”

“…The second will correct the system if one fails during the iterative process. Author's Name Derivative-free Matrix-free Double Direction Double step length Hybridization System of nonlinear equations Dennis and Schnabel [4] no no no no no no Li and Fukushima [9] yes no no no no yes Yuan and Xiwen [20] yes no no no no yes Waziri et al [19] yes no no no no yes Duranovic [11] yes yes yes no no no Halilu and Waziri [6] yes yes yes no no yes Duranovic and Filipovic [12] yes yes yes no no no Halilu and Waziri [7] yes yes yes no no yes Petrovic and Stanimirovic [15] yes yes yes no no no petrovic [13] yes yes yes yes no no petrovic et al [16] yes yes yes no yes no petrovic [14] yes yes yes yes yes no Abdullahi et al [ The followings are some of the contributions of this paper.…”