A new family of conjugate gradient methods for unconstrained optimization

Abstract

Conjugate gradient methods are well known and popular in unconstrained optimization. Numerous studies and modifications have been devoted by researchers to improve this method. In this paper, we introduced a new conjugate gradient coefficient ( k β ) and tested its performance using exact line search. Numerical results based on number of iterations have shown our new k β performance is better or equivalent to the other six well known k β proposed by the early researchers. The results also suggest that this method possesses global convergence properties.

Another modified conjugate gradient coefficient with global convergence properties

“…Suppose that Assumption 1 holds, consider a CG method of the form (2)-(4), where KMAR  is defined using (14) and k  satisfies exact line search then,…”

“…Therefore, in recent years, different researchers engaged on modifying or suggestion of a new formula for CG method that possess good numerical result and global convergent properties. For good references of CG methods with significant results, please refer to Hager and Zhang [16], Dai and Yuan [8], Andrei [7] and Rivaie et al [14].…”

A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches

“…For good references of CG methods with significant findings, please refer to Hager and Zhang [28], Sun and Zhang [11], Birgin and Martinez [3], Dai and Yuan [33], Yuan and Wei [6], Andrei [23], Shi and Guo [37], and Wei et al [39]. For a good compilation and comparative study of newer CG methods, please refer to Andrei [22,24] and Rivaie et al [18]. For a good explanation of classical CG method, please refer to Dai [29].…”

A new family of conjugate gradient coefficient with application

“…The first group comprises of PR, HS, RMIL and LS while in the second group we have FR, DY and CD. It is easy to see that the first group possesses the restart properties, whereas the second group does not have this characteristic [17][18]. In [20] has arranged the CG method into three distinct groups; the classical CG method, the scaled CG method and lastly the hybrid and parameterized CG methods.…”