In this investigation, we have compare the efficiencies of eight modelling package + solver combinations in solving Markowitz optimization models with none, linear, quadratic and regressed real-world trading cost models. (Pyomo, IPOPT) is our recommended open-sourced combination for its high efficiency, low variance in solving time and the ability to handle large-scale problems. The report is structured as follows:
- Section 1: we begin with a description of the setup of the evaluation experiments.
- Section 2: we present and interpret the results from the experiments.
- Section 3: we provide extra details about the recommended IPOPT solver.
- Section 4: we discuss qualitatively some additional properties of the modelling packages.
- Section 5: we discuss about the limitations of this investigation and directions for future work.
Figure 1: The mean solving times (in log-scale) vs. the number of assets (with sample standard deviations represented by the shaded area). Legends are sorted in ascending order of the solving times. MOSEK (commercial) is the solver that consistently delivers superior performance for all types of trading costs. Among the open-sourced solvers, (Pyomo, IPOTP) and (Pyomo, BONMIN) have very good performance for complex non-linear constraints (i.e. quadratic and generic cost), and outperforms some commercial solvers including GUROBI.
Figure 2: Boxplots of the solving times (in log-scale) of the modelling package + solver pairs. Legends are sorted in ascending order of solving times.