一族新的共轭梯度算法及其在SWP线搜索下的全局收敛性

A Class of New Conjugate Gradient Method and Its Global Convergence under the SWP Line Search

本文提出了一族计算β_k的新公式β_k^n(μ)(其中μ∈[0.1]为常量),证明了相应的共轭梯度法在σ∈(0.1/2)的SWP线搜索下具有全局收敛性,取μ=■为变量情形的β_k^n方法在SWP下也全局收敛。

The paper brings out a class of new formula βk^＊（μ）μ∈[0,1]is a constants）in calculating βk, and proofs the corresponding conjugate gradient method has global convergence under the SWPσ∈（0,1/2）line search.βk^＊method, taking μ=1/e‖gk-gk-1‖^k as variables, also has global convergence under SWP line search.