基于拟牛顿法的混合共轭梯度算法研究

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中图分类号：0224 文献标识码：A 文章编号：1674-0033(2025)06-0031-07

A Study on Hybrid Conjugate Gradient Method Based on Quasi Newton Method

XIE Ke-feng (College of Mathematical Sciences,Chongqing Normal University, Shapingba 401331, Chongqing)

Abstract: A new hybrid conjugate gradient method(FRCDDY method) is proposed for efficiently solving unconstrained optimization problems by making the conjugate gradient direction approximate the search direction of the memoryless BFGS quasi-Newton method,combined with parameters from the DY,CD,and FR methods.Under Wolfe line search，Armijo -type line search，and appropriate assumptions， the FRCDDY method is proven to satisfy the sufficient descent property and achieve global convergence for general functions.Extensive numerical experiments compared with other similar algorithms demonstrate that the FRCDDY method significantly outperforms its counterparts in computational efficiency.

Key words:unconstrained optimization; conjugate gradient method; memoryless BFGS quasi -Newton method; global convergence

对于无约束优化问题： minx∈Rnf(x) ，其中目标函数 f:Rn⟶R 连续可微。（剩余20385字）