High-speed human running data are difficult to acquire, limiting the availability of motion priors for high-speed humanoid running. To reduce dependence on motion capture and retargeting, this study proposes a framework that combines trajectory optimization with reinforcement learning. A planar multibody model generates reference motions across speeds subject to contact, periodicity, and actuator constraints. The optimized motions guide the training of a three-dimensional running policy through adversarial imitation and proximal policy optimization. Hardware experiments demonstrate treadmill running by the full-size BOLT humanoid at $10\mathrm{m}/\mathrm{s}$. In $2\mathrm{s}$ simulation windows under a $10\mathrm{m}/\mathrm{s}$ forward velocity command, comparison with a policy trained on retargeted human motions shows a more balanced distribution of joint loads relative to actuator capacity. The coefficient of variation of joint root-mean-square (RMS) utilization decreases from $0.397$ to $0.317$ across twelve joints, a reduction of $20.1\%$, with a corresponding reduction of $35.6\%$ across the six leg joints. These results support trajectory optimization as an effective source of motion priors for high-speed humanoid running and demonstrate a route from reference generation to hardware deployment without high-speed human motion data.