Efficient solution of fmincg without providing gradient? I'm working on multiclass logistic regression model with a large number of features (numFeatures > 100). Using a Maximum Likelihood Estimation based on the cost function and gradient, the fmincg algorithm solves the problem quickly. However, I'm also experimenting with a different cost function and do not have a gradient.

Is there a good way to speed up the calculation process? E.g., is there a different algorithm or fmincg setting that I can use?
If you do not have a gradient available, but the problem is convex, you can use the Nelder-Mead simplex method. It is available in most optimization packages, for example in scipy.optimize.