[Ipopt] about state variable and control variable in IPOPT

[Tony Kelman]

You can do either approach. If you have a long time horizon or complicated 
state constraints it might be beneficial to include both state and input 
variables in your optimization variable vector, and enforce your system 
dynamics as equality constraints. So z = [x; u], and you want to minimize 
f(z) s.t. g(z) = 0, h(z) <= 0. In this form the Jacobian of g and h would 
depend on both x and u. Depending on your problem structure, it's often 
better to let Ipopt handle solving equality constraints for you, rather than 
trying to do anything too clever with solving for x as a function of u at 
every iteration, which may have been what you were asking about?


-----Original Message----- 
From: Philipp Bender
Sent: Tuesday, October 28, 2014 12:23 AM
To: ipopt at list.coin-or.org
Subject: Re: [Ipopt] about state variable and control variable in IPOPT

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Hello Kayan,

so you want to solve an optimal control problem with IpOpt?

Like: what is the best action u, given state x? (Maximize expected
reward or some such?)

I don't know if your approach is feasible at all, but if you intend
what I stated above, I think you should not make x part of your
optimization parameters, since you are interested in u. Then you have
a "normal" optimization problem, but with properties I am not aware of.

Best regards,
Philipp

- -- 
Dipl.-Ing. Philipp Bender
Wissenschaftlicher Mitarbeiter
ISPE/MPS

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