scholarly journals A new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization

2013 ◽  
Vol 239 ◽  
pp. 396-405 ◽  
Author(s):  
Ioannis E. Livieris ◽  
Panagiotis Pintelas
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
New Class ◽  
Secant Equation ◽  
Spectral Conjugate Gradient ◽  
Modified Secant Equation

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.

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.

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