A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization
Optimization and Control
2017-05-08 v4
Abstract
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.
Cite
@article{arxiv.1507.05914,
title = {A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization},
author = {Christoph Buchheim and Marianna De Santis and Francesco Rinaldi and Long Trieu},
journal= {arXiv preprint arXiv:1507.05914},
year = {2017}
}