<p>The Polak–Ribière–Polyak (PRP) conjugate gradient method, while renowned for its practical efficiency among classical conjugate gradient algorithms, suffers from certain theoretical limitations that have motivated numerous modifications. One notable variant, the Rivaie–Mustafa–Ismail–Leong (RMIL) method, modifies the denominator of the PRP conjugate parameter and retains the anti-jamming property, but guarantees the sufficient descent condition—and consequently global convergence—only under exact line searches. To fully preserve the computational strengths of the RMIL scheme while overcoming its theoretical shortcomings, we introduce a novel spectral modification integrated within the non-linear conjugate gradient framework. Motivated by quasi–Newton principles and the classical secant condition, we derive a dynamic spectral parameter that enables the systematic projection of the search direction onto a subspace orthogonal to the objective gradient. This projection mechanism guarantees a strict sufficient descent condition at every iteration, completely independent of the line search strategy or the convexity of the objective function. A rigorous global convergence proof is provided for general non-linear objective functions, and the theoretical worst-case computational complexity of the proposed algorithm is established under the Armijo line search framework. We comprehensively evaluate its performance against state-of-the-art conjugate gradient baselines on a standard benchmark suite of CUTEr test functions, utilizing Dolan–Moré performance profiles for rigorous structural comparison. To further demonstrate its practical utility, the framework is applied to a representative real-world task in compressed sensing sparse signal recovery. The empirical findings conclusively highlight the superior convergence acceleration, numerical robustness, and practical efficiency of the proposed algorithm.</p>