What should be the optimization method for my case?

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I have an optimization problem which I minimize rms of velocity output of ODE function. When optimization runs, in each iteration first-order optimality goes high and low and repeats. I have inequality constraints, 5 for positions and, 5 for velocities. What method should it be to solve my problem?
Note: The lowest value for rms of velocity is 0 but it means there is no movement at all but I consider it in my constraints.
Thank you for help.

Accepted Answer

Alan Weiss
Alan Weiss on 29 Apr 2021
For such a general question I can give only general advice. See the topics Optimizing a Simulation or Ordinary Differential Equation and, perhaps (though it might not be applicable), Fit ODE, Problem-Based and Fit an Ordinary Differential Equation (ODE) and Optimize an ODE in Parallel (uses Global Optimization Toolbox, but you can use fmincon as well).
I hope this helps in some way,
Alan Weiss
MATLAB mathematical toolbox documentation
  5 Comments
Alan Weiss
Alan Weiss on 11 May 2021
Just one more thought. Perhaps you should not be using a fixed-step ODE solver. You can always get the solution at any times you like by using deval. Perhaps the solution process would be more reliable using a variable-step solver, possibly even one designed for stiff equations such as ode15s.
But maybe you know all this already. Sorry for wasting your time if so.
Alan Weiss
MATLAB mathematical toolbox documentation
Orcan Maktal
Orcan Maktal on 11 May 2021
I will try what you offer. I appreciate how fast you reply and bring ideas kind sir. Thank you, have a nice day.

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