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The FREE keyword is used in the METHODS section of your model when you want to un-fix a variable, such that ASCEND's solver will attempt to find its value by solving for it. The sense of the word 'free' here is 'to liberate'.

Often the FREE statement is not required, because by default all variables in a model are FREE when the model is created. You might sometimes want to write METHODS that re-configure your model in certain ways. Following the example from the FIX page, you might, for example, create the following additional METHOD:

(* add this to the example on the FIX page *)
METHOD solve_x;

    (* reconfigure the model to solve for x such that y=0 *)
    FREE x;
    FIX y;
    y:= 0;

END solve_x;

See also FIX.