A new two-parameter family of nonlinear conjugate gradient methods

作者：Sellami B^*; Laskri Y; Benzine R

来源：Optimization, 2015, 64(4): 993-1009.

DOI：10.1080/02331934.2013.830118

• 65K05
• 90C30
• 90C26
• 90C25
• 90C27
• global convergence
• line search
• unconstrained optimization
• conjugate gradient method

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed.

• 出版日期2015-4-3