Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs

This paper studies a scenario-based mean-CVaR portfolio optimization problem with nonconvex transaction costs. This problem can be framed as a mixed integer linear programming (MILP) problem by making a piecewise linear approximation of the transaction cost function. Nevertheless, large-scale problems are computationally intractable even with state-of-the-art MILP solvers. To efficiently solve them, we devised a subgradient-based cutting plane algorithm. We also devised a two-phase cutting plane algorithm that is even more efficient. Numerical experiments demonstrated that our algorithms can attain near-optimal solutions to large-scale problems in a reasonable amount of time.