Scalable Mean-Variance Portfolio Optimization via Subspace Embeddings and GPU-Friendly Nesterov-Accelerated Projected Gradient
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| Format: | Preprint |
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2026
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| author | Niu, Yi-Shuai Wang, Yajuan |
| author_facet | Niu, Yi-Shuai Wang, Yajuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable Mean-Variance Portfolio Optimization via Subspace Embeddings and GPU-Friendly Nesterov-Accelerated Projected Gradient Niu, Yi-Shuai Wang, Yajuan Optimization and Control Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing Machine Learning Numerical Analysis 91G10, 90C20, 90C25, 90C06, 65K05, 65F55, 65Y05 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. |
| title | Scalable Mean-Variance Portfolio Optimization via Subspace Embeddings and GPU-Friendly Nesterov-Accelerated Projected Gradient |
| topic | Optimization and Control Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing Machine Learning Numerical Analysis 91G10, 90C20, 90C25, 90C06, 65K05, 65F55, 65Y05 |
| url | https://arxiv.org/abs/2604.02917 |