[Ipopt] about state variable and control variable in IPOPT

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Hi,everyone:
  Now I am learning IPOPT software. I have a question. for the objective function min f(x,u), here the x means state variables, while the u means the 
         control variables. First in IPOPT  I set x and u as state variables. Howerver, can I only treat the x in Jacobian Matrix   of the constraint equation(not
 treat the u in the  Jacobian Matrix), and get the x variable   by the equality constraint equation. That is to say, the change of u cause the change of x by  
the constraint eqution.  
  in the Hessian and gradient of the objective, I treat the x and u together.
  I don't know whether it is feasible.
  
  Best Regards
  Yours
  Kaiyan Pan
   
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