Many SAS statistical procedures cannot do regression with constrains. For example, a spline regression with unknown location of a knot.

The regression lines(two lines) will be

y=b0+b1*x    for x<=xz;
y=bb0+bb1*x   for x>=xz;

suject to:   b0+b1*xz=bb0+bb1*xz

Here b0 b1 xz bb0 bb1 are all unknown parameters.

In proc optmodel, the constrain can be easily incorporated. See example below.



%let n=200;

data t1;
   do i=1 to &n;
      x=ranuni(1230)*4;
      x=sign(x)*x;
      y=1+1*x*x+rannor(123);
      x0=1;
      output;
    end;
    keep y x x0;
run;

proc reg data=t1;
model y=x;
run;
quit;

proc optmodel;
   set I = 1 .. &n;
   number y{I};
   number x{I};
   number x0{I};
   read data t1 into [_n_] y x x0;
   var b0, b1;
   min f =
      sum{k in I}
         ( y[k] - (b0*x0[k] + b1*x[k]))**2;

reset printlevel=2;
   solve with nlp;
         
   solve with qp;
   print f b0 b1;
quit;


proc optmodel;
   set I = 1 .. &n;
   number y{I};
   number x{I};
   number x0{I};
   read data t1 into [_n_] y x x0;
   var b0, b1 , xz, bb0, bb1;
   
         
   min f =sum{k in I} ( ( x[k]< xz )* ( y[k] - (b0*x0[k] + b1*x[k]))**2                              
                       + ( x[k]>= xz )* ( y[k] - (bb0*x0[k] + bb1*x[k]))**2 );

   con coef: b0+b1*xz=bb0+bb1*xz;
reset printlevel=2;
   solve with nlp;      
   print f b0 b1 xz bb0 bb1;
quit;