Portfolio construction as linearly constrained separable optimization

Mean–variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum nonzero position trade sizes. We propose a heuristic algorithm for such based the alternating direction method of multipliers (ADMM). This allows solve times in tens to hundreds milliseconds with around 1000 securities 100 risk factors. also obtain bound achievable performance. Our are both derived from similar results other objective affine equality constraints. discuss concrete implementation case where terms piecewise quadratic, we empirically demonstrate its effectiveness tax-aware construction.