AI 中文总结
该研究针对带线性与基数约束的投资组合优化问题，提出安全筛选规则，通过推导资产特定得分固定二元变量，在S&P 500等数据集上显著提升了优化的计算效率。
AI 中文摘要
在投资组合优化中，基数约束（限制持有的资产数量）在降低监控和交易成本方面发挥关键作用，但由此产生的问题是NP难的，随着候选资产数量增加，全局求解的计算难度会变大。安全筛选通过在优化前固定决策变量且不排除任何全局最优解来解决这一难题，在保留最优性保证的同时减小问题规模。我们针对具有凸二次目标函数和线性约束的基数约束投资组合优化问题提出安全筛选规则，利用L2正则项的透视松弛与Fenchel对偶，推导了包含线性约束拉格朗日乘子的资产特定得分；结合基于松弛的下界与可行解上界，这些得分可安全地将资产选择的二元变量固定为0或1。在S&P 500和Russell 2000数据集上的实验表明，在具有挑战性的案例中，尤其是在中等或强正则化以及宽松度较低的收益要求下，计算效率有显著提升。这些结果证明，安全筛选作为一种保留最优性的预处理技术，能大幅提升大规模基数约束投资组合优化的计算效率。
英文摘要
In portfolio optimization, a cardinality constraint, which limits the number of assets held, plays a key role in cutting down monitoring and transaction costs. However, the resulting problem is NP-hard and becomes computationally difficult to solve globally as the number of candidate assets grows. Safe screening addresses this difficulty by fixing decision variables before optimization without excluding any globally optimal solution, thereby reducing the problem size while preserving optimality guarantees. We propose safe screening rules for cardinality-constrained portfolio optimization with a convex quadratic objective function and linear constraints. Using a perspective relaxation of the L2-regularization term and Fenchel duality, we derive asset-specific scores that incorporate the Lagrange multipliers of the linear constraints. Combined with a relaxation-based lower bound and a feasible-solution upper bound, these scores safely fix binary asset-selection variables to zero or one. Experiments on S&P 500 and Russell 2000 datasets show substantial computational improvements on challenging cases, particularly under moderate or strong regularization and less stringent return requirements. These results demonstrate the effectiveness of safe screening as an optimality-preserving preprocessing technique that greatly boosts computational efficiency in large-scale cardinality-constrained portfolio optimization.
Comments8 pages, 2 tables, 1 figure
