I am solving an optimization problem using fmincon (interior point method). The gradient, jacobian and hessian are analytically calculated. The optimization algorithm takes takes about 900 iterations to converge to a solution. The problem size consists of 200 varaibles and 315 constraints. On inspecting the hessian of the Lagrangian, the condition number was around 1e12 to 1e16, though I didn't see any wanring from fmincon. What could be the issue here? I can post more information if required.
Any theoretical cues why the solver converges slowly? Are there any metrics that can point out the slow convergence?
Is there any issue with problem itself? I find the condition number very high and the problem can be ill-posed.