There are also several selectable line search methods. A Trust Region method is also available which prevents saddle point solutions.
Gradients can be user-provided or numerically calculated.
It is thus ideal for large scale Monte Carlo or bootstrap simulations. CO also contains a special technique for semi-definite problems, and thus it will solve the Markowitz portfolio allocation problem for a thousand stocks even when the covariance matrix is computed on fewer observations than there are securities. Because CO handles general nonlinear functions and constraints, it can solve a more general problem than the Markowitz problem. This model is solved for and the efficient frontier is the plot of on the vertical axis against on the horizontal axis. The portfolio weights in describe the optimum distribution of portfolio resources across the securities given the amount of risk to return one considers reasonable.