Generalizability of the Bartholomew et al. (2009) specialised algorithm beyond mean–variance

Determine whether the specialised algorithm developed by Bartholomew et al. (2009) for solving a mixed non-convex portfolio selection model—specifically, the mean–variance model with buy-in thresholds and lot constraints and without transaction costs—can be generalised to other optimisation criteria beyond the mean–variance objective used in that work.

Background

Within the discussion of single-stage mixed formulations, Bartholomew et al. (2009) are cited for proposing a mixed non-convex formulation addressing the mean–variance problem with buy-in thresholds and lot constraints, but omitting transaction costs. Although they devised a specialised algorithm tailored to that objective and structure, the paper notes that its broader applicability remains unresolved.

This uncertainty is relevant in the paper’s context because the authors argue that many single-stage formulations become computationally difficult or numerically fragile. If the Bartholomew et al. (2009) algorithm could be generalised to alternative portfolio objectives (e.g., CVaR, MAD, SSD), it might offer a unifying algorithmic path for realistic constraints; if not, it reinforces the need for approaches like the proposed two-stage framework that remain agnostic to the specific optimisation criterion.