scholarly journals TWO MODIFIED HYBRID CONJUGATE GRADIENT METHODS BASED ON A HYBRID SECANT EQUATION

2013 ◽  
Vol 18 (1) ◽  
pp. 32-52 ◽  
Author(s):  
Saman Babaie-Kafaki ◽  
Nezam Mahdavi-Amiri
Keyword(s):  
Conjugate Gradient ◽  
Gradient Methods ◽  
Numerical Results ◽  
Conjugate Gradient Methods ◽  
Globally Convergent ◽  
Secant Equation ◽  
Hybrid Secant Equation

Taking advantage of the attractive features of Hestenes–Stiefel and Dai–Yuan conjugate gradient methods, we suggest two globally convergent hybridizations of these methods following Andrei's approach of hybridizing the conjugate gradient parameters convexly and Powell's approach of nonnegative restriction of the conjugate gradient parameters. In our methods, the hybridization parameter is obtained based on a recently proposed hybrid secant equation. Numerical results demonstrating the efficiency of the proposed methods are reported.

AN ADAPTIVE CONJUGACY CONDITION AND RELATED NONLINEAR CONJUGATE GRADIENT METHODS

2014 ◽  
Vol 11 (04) ◽  
pp. 1350092 ◽  
Author(s):  
SAMAN BABAIE-KAFAKI
Keyword(s):  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Conjugacy Condition ◽  
Globally Convergent ◽  
Reasonable Solution ◽  
Secant Equation ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods ◽  
Adaptive Switch

In an attempt to find a reasonable solution for an open problem propounded by Andrei in nonlinear conjugate gradient methods, an adaptive conjugacy condition is proposed. The suggested condition is designed based on an implicit switch from a conjugacy condition to the standard secant equation, using an extended conjugacy condition proposed by Dai and Liao. Following the approach of Dai and Liao, two adaptive nonlinear conjugate gradient methods are proposed based on the suggested adaptive conjugacy condition. An interesting feature of one of the proposed methods is the adaptive switch between the nonlinear conjugate gradient methods proposed by Hestenes and Stiefel, and Perry. Under proper conditions, it is shown that one of the proposed methods is globally convergent for uniformly convex functions and the other is globally convergent for general functions. Numerical results demonstrating the effectiveness of the proposed adaptive approach in the sense of the performance profile introduced by Dolan and Moré are reported.

A class of globally convergent three-term Dai-Liao conjugate gradient methods

2020 ◽  
Vol 151 ◽  
pp. 354-366 ◽  
Author(s):  
Shengwei Yao ◽  
Qinliang Feng ◽  
Lue Li ◽  
Jieqiong Xu
Keyword(s):  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Globally Convergent

scholarly journals Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Gradient Methods ◽  
Numerical Results ◽  
Conjugate Gradient Methods ◽  
Descent Condition ◽  
Wolfe Line Search ◽  
Large Scale Unconstrained Optimization

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent conditiongkTdk≤-1-1/4θkgk2  θk>1/4and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.

scholarly journals A new family of Dai-Liao conjugate gradient methods with modified secant equation for unconstrained optimization

2021 ◽  
Author(s):  
Yutao Zheng
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Conjugacy Condition ◽  
New Family ◽  
Secant Equation ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Modified Secant Equation

In this paper, a new family of Dai-Liao--type conjugate gradient methods are proposed for unconstrained optimization problem. In the new methods, the modified secant equation used in [H. Yabe and M. Takano, Comput. Optim. Appl., 28: 203--225, 2004] is considered in Dai and Liao's conjugacy condition. Under some certain assumptions, we show that our methods are globally convergent for general functions with strong Wolfe line search. Numerical results illustrate that our proposed methods can outperform some existing ones.

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