A New Conjugate Gradient Coefficient for Large Scale Nonlinear Unconstrained Optimization

Abstract Conjugate gradient (CG) methods have played an important role in solving largescale unconstrained optimization due to its low memory requirements and global convergence properties. Numerous studies and modifications have been devoted recently to improve this method. In this paper, a new modification of conjugate gradient coefficient ( k β ) with global convergence properties are presented. The global convergence result is established using exact line searches. Preliminary result shows that the proposed formula is competitive when compared to the other CG coefficients. Mathematics Subject Classification: 65K10, 49M3

A comparison on classical-hybrid conjugate gradient method under exact line search

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time

Sediment Variation along the East Coast of Peninsular Malaysia

The northeast monsoon season (NEMS), which occurs between November and March every year, brings heavy rains and strong wind to the east coast of Peninsular Malaysia. Large sediment resuspension during this season is caused by high waves and river discharge carried by the river to the sea. Sediment is defined in this research as both organic and inorganic materials. Remote sensing reflectance (Rrs) of the Moderate Resolution Spectroradiometer (MODIS) 667 nm channel is used in this study as a Total Suspended Sediment (TSS) index. The data was acquired from Aqua satellite with 9 km resolution. The study was conducted along the eastern coast of Peninsular Malaysia over the period of 2002-2012. The result shows that TSS along the Peninsular Malaysia coastline and the river mouth is highly seasonal. The highest TSS is observed during NEMS with the peak value in November-December every year

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

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

A New Conjugate Gradient Method with Exact Line Search

Abstract Conjugate gradient (CG) methods have been practically used to solve large-scale unconstrained optimization problems due to their simplicity and low memory storage. In this paper, we proposed a new type of CG coefficients

An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions

Global Convergence of a New Coefficient Nonlinear Conjugate Gradient Method

Nonlinear conjugate gradient (CG) methods are widely used in optimization field due to its efficiency for solving a large scale unconstrained optimization problems. Many studies and modifications have been developed in order to improve the method. The method is known to possess sufficient descend condition and its global convergence properties under strong Wolfe-Powell search direction. In this paper, the new coefficient of CG method is presented. The global convergence and sufficient descend properties of the new coefficient are established by using strong Wolfe-Powell line search direction. Results show that the new coefficient is able to globally converge under certain assumptions and theories

A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization

In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations.<br

A comparative study of three new conjugate gradient methods with exact line search

Conjugate Gradient methods play an important role in solving unconstrained optimization, especially for large scale problems. In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR, PRP with three new B_k . These three new B_k possess global convergence properties using the exact line search. Preliminary numerical results show that the three new B_k are very promising and efficient when compared to CG coefficients FR, PRP

A comparative study of two new conjugate gradient methods

In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR , PRP with two new B_k .These two new B_k possess global convergence properties using the exact line search. Preliminary numerical results show that, the two new B_k is very promising and efficient when compared to CG coefficients FR , PRP