[Ipopt] Few questions about IPOPT convergence

[Atri Dutta]

Hi All, 

I have been using IPOPT to solve trajectory optimization problems for a while now, but I guess I am still in a learning phase. I am using IPOPT 3.10 and the Matlab interface. I have a few questions and I would appreciate your comments: 

1) When I solve minimum time problems, I obtain pretty good convergence if I provide analytic expressions for the Hessian. Keeping everything unchanged, if I use the option to approximate Hessian, the program does not converge most of the time. What could a possible reason for this? What is a good strategy to ensure convergence when using Hessian approximation option? 

2) If we keep the problem same in terms of constraints and variable bounds but change the objective (the cost in this case cannot be computed analytically and hence I can no longer provide exact Hessian), the problem does not converge at all. The modified problem differs only in the objective function, hence I  provide as an initial guess previously obtained minimum-time solutions that should be feasible for the modified problem. As IPOPT runs and tries to solve the problem, it attains primal feasibility (with respect to given tolerance) fairly quickly and does reduce the objective value at each step. However, the program either ends up in "Restoration Failed" or exceeds the maximum iterations with a solution that is primal feasible but dual infeasible. What might be the reason for the trouble in achieving dual feasibility? 

3) What is the usual strategy when one encounters Restoration Failed? 

Your comments would be really helpful. 

Best Regards, 
Atri. 

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Atri Dutta 
Mechanical and Aerospace Engineering, 
Princeton University. 
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