<p>The global convergence of the DFP algorithm under the weak Wolfe–Powell (WWP) line search for uniformly convex functions remains an open problem, and it was regarded by Nocedal and Fletcher in the early 1990s as the first open problem in unconstrained optimization. This problem has also been included by Li and Zhang among the ten thousand most difficult scientific problems. This study introduces a novel projected DFP algorithm (Algorithm 2) by constructing a projection parabolic condition and an alternating update strategy, which innovatively integrates projection mechanisms with canonical DFP updates. The DFP direction is adopted if it satisfies the proposed projection parabolic condition. Otherwise, a corrected direction ensuring convergence is generated via projection. We rigorously establish the global convergence of Algorithm 2 under the WWP line search for uniformly convex functions and validate its efficacy through numerical experiments. In the standard optimization experiment, Algorithm 2 demonstrates superior performance and robustness compared to both classical DFP and an improved damped DFP algorithm. Furthermore, when applied to the hydrologic engineering model, Algorithm 2 yields optimal approximation solutions that diverge from those of existing methods. To further assess its versatility, we evaluate Algorithm 2 on two machine learning models and find that it typically matches or outperforms existing methods.</p>