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.
2018, JOURNAL OF GLOBAL OPTIMIZATION, Pages 625-644 (volume: 3)
A Frank–Wolfe based branch-and-bound algorithm for mean-risk optimization (01a Articolo in rivista)
Buchheim Christoph, De Santis Marianna, Rinaldi Francesco, Trieu Long
Gruppo di ricerca: Continuous Optimization