About Dualize( )

[Kris]

Hello Prof

Thank you for always helping me in good faith. Today, I tried to figure out the command dualize( ) with help command, and the matlab returned me the following information >> help dualize
  dualize Create the dual of an SDP given in primal form
 
  [Fd,objd,X,t,err] = dualize(F,obj,auto)
 
  Input
   F    : Primal constraint in form AX=b+dt, X>0, t free.
   obj  : Primal cost CX+ct
   auto : If set to 0, YALMIP will not automatically handle variables
         and update variable values when the dual problem is solved.
   extlp: If set to 0, YALMIP will not try to perform variables changes in
          order to convert simple translated LP cones (as in x>1) to
          standard unit cone constraints (x>0)
 
  Output
   Fd  : Dual constraints in form C-A'y>0, c-dy==0
   obj : Dual cost b'y (to be MAXIMIZED!)
   X   : The detected primal cone variables
   t   : The detected primal free variables
   err : Error status (returns 0 if no problems) I wanna ask you about X   : The detected primal cone variables  and  t   : The detected primal free variables. What are the role of detected variables and free variables? I guess the free variables may similar to slack variables, which can transform the problem into an assumed form of Yalmip? Although you have told me that don't worry about the details in Automatic Dualize, I still wonder what detected and free use for. I'd appreciate it if you can teach me. Best wish Kris

[Johan Löfberg]

Have you read the referenced paper https://yalmip.github.io/reference/lofberg2009b/. If not, do that.

[Kris]

Thanks Prof, I will read the referenced paper.