Question

[Peter230655]

I am trying an inverted pendulum, but in 3D, and I get this message:

message from optimizer: b'Maximum number of iterations exceeded (can be specified by an option).'

I cannot find from the documentation where I could specify the number of operations.

Thanks for any help!

[tjstienstra]

These kinds of settings are in ipopt. Refer to https://coin-or.github.io/Ipopt/OPTIONS.html for more ipopt settings. To specify an option you can use the Problem.add_option method. In this case you can change the maximum number of iterations using:

prob.add_option("max_iter", 4000)  # 3000 is the default

However, I would recommend that you look through your problem definition because it is most likely there is something wrong there.

[moorepants]

If you are hitting max iterations, it more likely means you need improvements to your optimal control problem design, initial guess, interval choice, etc. Optimization problems rarely converge with default inputs and settings. In these types of optimizations you often have to solve a series of simpler problems to generate a good initial guess for the final problem.

[Peter230655]

Thanks both of you!

1. Making num_nodes larger with given duration should help, right?
2. The result of the simpler problem would be the initial guess for the harder one, correct?
3. My experience with optimization problems is very, very limited. In general, is it easier to solve if fewer constraints are imposed? My first feeling is YES, but then again more constraints may limit the 'space to be searched' thus making it easier. I simply do not know. Thanks for any hints!

[tjstienstra]

1. Making num_nodes larger with given duration should help, right?

No, I would say that it actually makes it harder to solve in general. The optimization algorithm will require tuning more variables while also satisfying more constraints. At the same time, I should mention that too few nodes can make something impossible to solve.

2. The result of the simpler problem would be the initial guess for the harder one, correct?

Yes, there are various options (I know of):

• Just use np.zeros or np.random.randn
  • Really simple to implement, but is the worst as the optimization has to do everything
• Interpolate between the initial and final state constraints as an initial guess (might actually be a nice feature request)
  • This is my favourite as it is simple and can be implemented quickly
• Use the output of a forward simulation where you try to approximate the motion that should be done
  • This can be rather hard to get a good implementation of
• Use an initial guess derived from the solution of a simpler system.
  • Works probably best, but you will be required to solve multiple systems. If your guess is really good you may also want IPOPT to use something like a warm start (tells it that it is close to the actual solution)

3. My experience with optimization problems is very, very limited. In general, is it easier to solve if fewer constraints are imposed? My first feeling is YES, but then again more constraints may limit the 'space to be searched' thus making it easier. I simply do not know.

Mine is also limited, but I would also in general say that fewer constraints make it easier to solve a problem in the general case. My experience is that you should try to minimize your instance constraints.

[Peter230655]

Thanks!! What I am playing around with is the inverted pendulum attached to a cart, just in 3D. What I have done so far is this: I loop around the problem, starting with the pendulum being almost vertically up, and use the solution to this problem as initial guess for the pendulung a bit more away from the vertical, and so on. This seems to work fine until the pendulum is almost horizontal, but if it is below the horizontal it does not seem to work, yet. I will keep you posted as I run more trials.

[tjstienstra]

I can have a quick look at the problem definition if you like (feel free to mail it).

[Peter230655]

I sent by separate mail.