An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis

Published on Jun 15, 2020
· DOI :10.3390/MATH8060977
Siti Farhana Husin1
Estimated H-index: 1
Mohd Asrul Hery Ibrahim5
Estimated H-index: 5
Mohd Rivaie7
Estimated H-index: 7
This study employs exact line search iterative algorithms for solving large scale unconstrained optimization problems in which the direction is a three-term modification of iterative method with two different scaled parameters. The objective of this research is to identify the effectiveness of the new directions both theoretically and numerically. Sufficient descent property and global convergence analysis of the suggested methods are established. For numerical experiment purposes, the methods are compared with the previous well-known three-term iterative method and each method is evaluated over the same set of test problems with different initial points. Numerical results show that the performances of the proposed three-term methods are more efficient and superior to the existing method. These methods could also produce an approximate linear regression equation to solve the regression model. The findings of this study can help better understanding of the applicability of numerical algorithms that can be used in estimating the regression model.
📖 Papers frequently viewed together
42 Citations
2009ICCS: International Conference on Computational Science
7 Citations
#1Selvia Oktaviyani (LIPI: Indonesian Institute of Sciences)H-Index: 1
#2Wanwan Kurniawan (LIPI: Indonesian Institute of Sciences)H-Index: 1
Last. Fahmi (LIPI: Indonesian Institute of Sciences)H-Index: 9
view all 3 authors...
Shark fins are a very valuable product for international trade. This study aims to obtain the equations describing the relationship between fin length and the total length of silky shark. Using the total length at sexual maturity (Lm), the equation is then used to estimate the fin length associated with this Lm, which can then be included in the recommendation for international shark fin trades. Data collection was carried out from March 2018 to February 2019 at Tanjung Luar Fish Landing Port, W...
1 CitationsSource
#1Jinbao JianH-Index: 1
#2Lin YangH-Index: 1
Last. Meixing LiuH-Index: 1
view all 5 authors...
Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral para...
3 CitationsSource
#1Yan Pei (University of Aizu)H-Index: 11
#2Jun Yu (Kyushu University)H-Index: 6
Last. Hideyuki TakagiH-Index: 31
view all 3 authors...
We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing ...
8 CitationsSource
#1Chia-Nan WangH-Index: 17
#2Tien-Muoi LeH-Index: 3
Last. Han-Khanh NguyenH-Index: 4
view all 3 authors...
Many factors influence the efficiency and quality of transport works. In particular, consultants and construction contractors of these works play important roles, and critical factors directly affect the quality of traffic works. If the quality of consultancy and construction is good, the project will reduce the total investment; if the contractor is good, the completion time of the new project is guaranteed, thus reducing construction costs. The longer the construction time is, the higher the c...
4 CitationsSource
#1Mina TorabiH-Index: 1
#2M. M. HosseiniH-Index: 13
In this paper, three-step Taylor expansion, which is equivalent to third-order Taylor expansion, is used as a mathematical base of the new descent method. At each iteration of this method, three steps are performed. Each step has a similar structure to the steepest descent method, except that the generalized search direction, step length, and next iterative point are applied. Compared with the steepest descent method, it is shown that the proposed algorithm has higher convergence speed and lower...
6 CitationsSource
#1Nurul HajarH-Index: 2
#2Mustafa MamatH-Index: 15
Last. Ibrahim JusohH-Index: 2
view all 4 authors...
Nowadays, conjugate gradient (CG) methods are impressive for solving nonlinear unconstrained optimization problems. In this paper, a new CG method is proposed and analyzed. This new CG method satisfies descent condition and its global convergence is established using exact line search. Numerical results show that this new CG method substantially outperforms the previous CG methods. This new CG method is considered robust, efficient and provided faster and stable convergence.
7 CitationsSource
#3Mohd RivaieH-Index: 7
One of the earliest and the best method to minimize a function is the classical steepest descent (SD) method. In this paper, a new modification of SD method is suggested using a new search direction, d k. The numerical results are presented based on number of iterations and CPU time. It shows that the new d k are efficient when compared to the classical SD.
4 CitationsSource
#1Mohd Rivaie (UiTM: Universiti Teknologi MARA)H-Index: 7
#2Mustafa Mamat (UniSZA: Universiti Sultan Zainal Abidin)H-Index: 15
Last. Abdelrhaman Abashar (Red Sea University)H-Index: 4
view all 3 authors...
Conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. In this paper, we propose a new family of CG coefficients (βk) that possess sufficient descent conditions and global convergence properties. This new βk is an extension of the already proven β k RMIL from Rivaie et al. 19 (A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comp. 218(2012) 11323-11332). Global convergence result is e...
20 CitationsSource
Recently, sufficient descent property plays an important role in the global convergence analysis of some iterative methods. In this paper, we propose a new iterative method for solving unconstrained optimization problems. This method provides a sufficient descent direction for objective function. Moreover, the global convergence of the proposed method is established under some appropriate conditions. We also report some numerical results and compare the performance of the proposed method with so...
2 CitationsSource
#1Momin Jamil (BTH: Blekinge Institute of Technology)H-Index: 6
#2Xin-She Yang (Middlesex University)H-Index: 87
Test functions are important to validate and compare the performance of optimisation algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties to be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimisation problems with diverse prop...
700 CitationsSource
Cited By0