We develop a sketch-based factor reduction and a Nesterov-accelerated projected gradient algorithm (NPGA) with GPU acceleration, yielding a doubly accelerated solver for large-scale constrained mean-variance portfolio optimization. Starting from the sample covariance factor $L$, the method combines randomized subspace embedding, spectral truncation, and ridge stabilization to construct an effective factor $L_{eff}$. It then solves the resulting constrained problem with a structured projection computed by scalar dual search and GPU-friendly matrix-vector kernels, yielding one computational pipeline for the baseline, sketched, and Sketch-Truncate-Ridge (STR)-regularized models. We also establish approximation, conditioning, and stability guarantees for the sketching and STR models, including explicit $O(\varepsilon)$ bounds for the covariance approximation, the optimal value error, and the solution perturbation under $(\varepsilon,δ)$-subspace embeddings. Experiments on synthetic and real equity-return data show that the method preserves objective accuracy while reducing runtime substantially. On a 5440-asset real-data benchmark with 48374 training periods, NPGA-GPU solves the unreduced full model in 2.80 seconds versus 64.84 seconds for Gurobi, while the optimized compressed GPU variants remain in the low-single-digit-second regime. These results show that the full dense model is already practical on modern GPUs and that, after compression, the remaining bottleneck is projection rather than matrix-vector multiplication.

翻译：我们提出了一种基于草图化的因子降维方法与Nesterov加速投影梯度算法（NPGA），并采用GPU加速，从而为大规模约束均值-方差投资组合优化问题提供双加速求解器。该方法从样本协方差因子$L$出发，通过结合随机子空间嵌入、谱截断和岭稳定化技术构造有效因子$L_{eff}$。随后，利用标量对偶搜索与GPU友好的矩阵-向量核计算结构化的投影，求解由此产生的约束问题，形成一套涵盖基准模型、草图化模型和草图-截断-岭（STR）正则化模型的统一计算流程。我们还为草图化和STR模型建立了逼近、条件数和稳定性保证，包括在$(\varepsilon,δ)$-子空间嵌入下关于协方差逼近、最优值误差和解扰动的显式$O(\varepsilon)$界。在合成数据与真实股票收益率数据上的实验表明，该方法在保持目标函数精度的同时显著缩短了运行时间。在包含5440个资产与48374个训练周期的真实数据基准测试中，NPGA-GPU以2.80秒求解未约减的全模型，而Gurobi需要64.84秒；经过优化的压缩GPU变体则保持在个位数秒级。这些结果表明，全密集模型在现代GPU上已具备实用性，且在压缩后，剩余的计算瓶颈是投影运算而非矩阵-向量乘法。