This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by means of the moment-based uncertainty set of probability distributions of asset returns. To exactly solve large-scale problems, we propose a specialized cutting-plane algorithm that is based on bilevel optimization reformulation. We prove the finite convergence of the algorithm. We also apply a matrix completion technique to lower-level SDO problems to make their problem sizes much smaller. Numerical experiments demonstrate that our cutting-plane algorithm is significantly faster than the state-of-the-art MISDO solver SCIP-SDP. We also show that our portfolio optimization model can achieve good investment performance compared with the conventional mean-variance model.

翻译：本文研究一种分布上稳健的组合优化模式,对限制投资资产的数量有基本限制。我们通过基于时间的资产回报概率分配不确定组合,将这一模式发展成混合整数半无限制优化(MISPO)问题。为了确切解决大规模问题,我们建议一种基于双级优化重组的专门切割机算法。我们证明算法的有限趋同。我们还对较低层次的SDO问题应用矩阵完成技术,使其问题规模小得多。数字实验表明,我们的切割机算法比最先进的MISPODO SCIIP-SDP还快得多。我们还表明,我们的组合优化模式能够取得与常规平均变差模式相比的良好投资业绩。