Unfortunately, SAS does not provide gradian and hessian for a given function. If the function is explicitly defined, one could provide the information(simple math mostly) to some sas procs. Otherwise most sas procs will calculate it for you WITHIN those procs using finite difference method.

Here is an example of the Newton-Raphson methed in Finite difference formulae for a quadratic equation. I hope this sheds light on the approach.

HTH.


501  ****Newton's Method;
502  ***Finite difference formulae;
503  ***example f(x)=x^2 + x -3;
504
505  ***min f(-0.5) = -3.25   ;
506
507  %macro f(x);
508       (&x)**2+(&x)-3
509  %mend;
510
511  %macro f1st(x, h);
512   (  (  %f(&x+&h) ) -  (  %f(&x-&h)  ) )/(2*&h)
513  %mend;
514
515  %macro f2nd(x, h);
516   (  (  %f(&x+&h)  )  - 2*( %f(&x) ) +  ( %f(&x-&h) ) )/(&h**2)
517  %mend;
518
519  data _null_;
520
521   x0=90;h=0.006;
522   do i = 1 to 100;
523       z1=%f1st(x0, h); z2=%f2nd(x0, h);
524
525      x=x0 - z1 /z2;
526       if abs  ( %f1st(x, h) )  <1e-6 then do;
527            *evaluate function values at optimal point;
528            z0=%f(x);  z1=%f1st(x, h);  z2=%f2nd(x, h);
529            put i= x= z0= z1= z2=;
530            stop;
531       end;
532       else x0=x;
533   end;
534  run;

i=1 x=-0.499999835 z0=-3.25 z1=3.2998479E-7 z2=2
NOTE: DATA statement used (Total process time):
      real time           0.00 seconds
      cpu time            0.00 seconds