Globally convergent Polak-Ribiere-Polyak conjugate gradient methods under a modified Wolfe line search

作者：Yu, Gaohang^*; Guan, Lutai; Wei, Zengxin

来源：Applied Mathematics and Computation, 2009, 215(8): 3082-3090.

DOI：10.1016/j.amc.2009.09.063

• Unconstrained optimization
• Conjugate gradient method
• Global convergence

It is well known that global convergence has not been established for the Polak-Ribiere-Polyak (PRP) conjugate gradient method using the standard Wolfe conditions. In the convergence analysis of PRP method with Wolfe line search, the (sufficient) descent condition and the restriction beta(k) >= 0 are indispensable (see [4,7]). This paper shows that these restrictions could be relaxed. Under some suitable conditions, by using a modified Wolfe line search, global convergence results were established for the PRP method. Some special choices for beta(k) which can ensure the search direction's descent property were also discussed in this paper. Preliminary numerical results on a set of large-scale problems were reported to show that the PRP method's computational efficiency is encouraging.

• 出版日期2009-12-15
• 单位广西大学; 赣南师范大学; 中山大学