$TITLE Duffin's duality gap example
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 SETS     J         index      / I1 * I2 / ;

 VARIABLES
      X(J)   unknowns
      Z      optimal value  ;

 EQUATIONS 
    COST   define objective function
    CONSTRAINT single constraint nonlinear ;
 
 COST..  Z =E= EXP(-X('I2')) ;
 CONSTRAINT.. SQRT( SQR(X('I1')) + SQR(X('I2')) ) - X('I1') =L= 0 ;

MODEL DUFFIN /ALL/;

 SOLVE DUFFIN  MINIMIZING Z USING NLP;