The _OROPTMILP_ macro variable contains this information.  You can use the following DATA step to append the desired values to a text file:
data _null_;
   file 'myfile.txt' mod;
   oroptmilp = symget('_OROPTMILP_');
   index = index(oroptmilp, 'OBJECTIVE');
   objective = scan(substr(oroptmilp, index), 2, ' =');
   index = index(oroptmilp, 'RELATIVE_GAP');
   relative_gap = scan(substr(oroptmilp, index), 2, ' =');
   put objective relative_gap;
run;
By the way, in PROC OPTMODEL these values are more simply accessible as
_OROPTMODEL_NUM_['OBJECTIVE'] and _OROPTMODEL_NUM_['RELATIVE_GAP'].