# A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization

arXiv: https://arxiv.org/abs/1810.10563 · HTML: https://mlsanity.com/paper/1810.10563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Stock Portfolio Optimization Using a Deep Learning LSTM Model](https://mlsanity.com/paper/2111.04709/) (2021)

## Abstract (arXiv)

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new approach to solve cardinality-constrained portfolio optimization problems, extending both Markowitz and conditional value at risk (CVaR) optimization models with cardinality constraints. We derive a continuous relaxation method for the NP-hard objective, which allows for very efficient algorithms with standard convergence guarantees for nonconvex problems. For smaller cases, where brute force search is feasible to compute the globally optimal cardinality- constrained portfolio, the new approach finds the best portfolio for the cardinality-constrained Markowitz model and a very good local minimum for the cardinality-constrained CVaR model. For higher dimensions, where brute-force search is prohibitively expensive, we find feasible portfolios that are nearly as efficient as their non-cardinality constrained counterparts.