# Cardinality-constrained Distributionally Robust Portfolio Optimization

arXiv: https://arxiv.org/abs/2112.12454 · HTML: https://mlsanity.com/paper/2112.12454/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2021.

## Built on by (most cited first, 4 of 4)

- [Robust Optimization with Diffusion Models for Green Security](https://mlsanity.com/paper/2503.05730/) (2025)
- [Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics](https://mlsanity.com/paper/2406.10250/) (2024)
- [Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty](https://mlsanity.com/paper/2609.11749/) (2026)
- [Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation](https://mlsanity.com/paper/2609.21427/) (2026)

## Abstract (arXiv)

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 ambiguity 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 robust optimization model based on the ellipsoidal uncertainty set.