A Frank–Wolfe based branch-and-bound algorithm for mean-risk optimization
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.