Memoryless three-term RMIL-type conjugate gradient method for solving unconstrained optimization and image denoising problems

This study introduces a modified version of the Rivaie-Mustafa-Ismail-Leong (RMIL) Conjugate Gradient Method (CGM), which produces a search direction similar to that of the memoryless BFGS Quasi-Newton approach. When exact line search (ELS) is applied, the method reverts to the original RMIL method. Additionally, for any line search with a constant $ \bar{t} \in [0, 1) $, the proposed method's direction fulfills the sufficient descent condition (SDC). The Global Convergence (GC) of the method is demonstrated for strongly convex objective functions using the weak Wolfe line search (WWLS). The effectiveness of the proposed methods are evaluated through two approaches. First, numerical experiments are conducted on Unconstrained Optimization Problem (UOP), where the proposed method displays comparable performance to existing CGMs which significantly outperforms under WWLS, achieving faster convergence. Second, the proposed methods are applied to Image Denoising Problem (IDP), further validating its practical applications. The results indicate that the proposed method holds strong theoretical and numerical promise for optimization challenges.