Optimization methods are widely used to obtain the numerical solution of the optimal control problems arising in scientific and engineering computation, especially for solving large-scale problems. In this paper, based on some modern and computationally efficient methods, a new conjugate gradient method ( named ICG method) is proposed for unconstrained optimization. Under the strong Wolfe line search (SWLS), the presented method is proven to be sufficient descent at each iteration. Moreover, we proved that the proposed method is globally convergent for arbitrary functions and the line search satisfies the strong Wolfe conditions. Numerical tests demonstrate the effectiveness of the ICG method when compared to certain existing methods in view of the Dolan and Mor´e performance profile. In particular, the practical application of this method in image restoration problems is explored.
Elhamid et al. (2026) studied this question.