Global Conference on Mathematics and Applications (GCMA)

Conjugate gradient (CG) methods are widely used in neural network training owing to their low memory requirements, although the classical Fletcher–Reeves (FR) method can converge slowly. In this work, we develop a modified FR-type CG algorithm in which a logistic mapping is applied to the FR coefficient and combined with the NPRP coefficient through a safeguarded parameter, ensuring that |β_j| ≤ β_j^FR. Under standard assumptions and the strong Wolfe line search, we prove that the generated directions satisfy the sufficient descent condition, with a constant depending only on the Wolfe parameter σ, and that the method is globally convergent. Numerical experiments on unconstrained CUTE test problems show reductions in iterations, function evaluations, and CPU time of 73.6%, 56.5%, and 87.9% relative to FR, and 11.2%, 5.3%, and 7.4% relative to NPRP. When applied to training a feedforward neural network for breast cancer classification (Wisconsin Diagnostic dataset), the method reaches an accuracy of 98.24%, and is compared with FR, NPRP, L-BFGS, and Adam. The proposed method thus offers a memory-efficient and theoretically supported alternative for neural network training