I am solving a high-dimensional optimization problem with an inequality constraint using blackboxoptim. The objective function is differentiable, but I cannot write down the Hessians by hand. The dimensionality is over 7000. I know the dimensionality is extremely high, so I am seeking advice on which way should I go to achieve better results and what alternative packages (besides blackboxoptim) to use:
- choose multiple starting points (achievable in blackboxoptim, but I suspect that many of these starting points will violate the inequality constraint, and I don’t know how to write codes to choose starting points that satisfy the inequality constraint);
- use a more efficient algorithm. Since the objective function is automatically differentiable, I wonder if it is possible to solve the problem without providing the Hessian matrix. If so, can I use NLOpt or JuMP instead?
- given the high dimensionality, multiplicity is expected. Any suggestions for dealing with multiplicity in optimization problems?
Thanks a bunch!!!