# A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization

arXiv: https://arxiv.org/abs/1507.05914 · HTML: https://mlsanity.com/paper/1507.05914/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2015.

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

- [Convex mixed-integer optimization with Frank-Wolfe methods](https://mlsanity.com/paper/2208.11010/) (2022)

## Abstract (arXiv)

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems by designing a branch-and-bound algorithm, where at each node, the continuous relaxation is solved by a non-monotone Frank-Wolfe type algorithm with away-steps. Experimental results on portfolio optimization problems show that our approach can outperform the MISOCP solver of CPLEX 12.6 for instances where a linear risk-weighting function is considered.