GRADIENT Statement

The NLP Procedure

GRADIENT Statement

GRADIENT variables ;

The GRADIENT statement defines the gradient vector which contains the first-order derivatives of the objective function f with respect to x₁, ... ,x_n. For more information, see the section "Derivatives". To specify the values of nonzero derivatives, the variables specified in the GRADIENT statement must be defined at the left-hand side of algebraic expressions in programming statements. For example,consider the Rosenbrock function:

       proc nlp tech=congra;
         min y;
         decvar x1 x2;
         gradient g1 g2;

         y1 = 10 * (x2 - x1 * x1);
         y2 = 1 - x1;

         y  = .5 * (y1 * y1 + y2 * y2);

         g1 = -200 * x1 * (x2 - x1 * x1) - (1 - x1); 
         g2 = 100 * (x2 - x1 * x1);
       run;

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