We construct an algorithm that allows to numerically obtain an investor's optimal portfolio under general preferences. In particular, the objective function and risks constraints may be driven by benchmarks (reflecting state-dependent preferences). We apply the algorithm to various classic optimal portfolio problems for which explicit solutions are available and show that our numerical solutions are compatible with them. This observation allows to conclude that the algorithm can be trusted as a viable way to deal with portfolio optimization problems for which explicit solutions are not in reach. This is joint work with Rob De Staelen (University of Ghent) and Steven Vanduffel (Vrije Universiteit Brussel).