JACNLC Statement

The NLP Procedure

JACNLC Statement

JACNLC variables ;

The JACNLC statement defines the Jacobian matrix for the system of constraint functions c₁(x), ... ,c_mc(x). The statements lists the mc*n variable names which correspond to the elements CJ_i,j, i = 1, ... ,mc, j = 1, ... ,n, of the Jacobian matrix by rows.

For example, the statements

  nlincon c1-c3;
  decvar  x1-x2;
  jacnlc  cj1-cj6;

correspond to the Jacobian matrix

$CJ = [ CJ1 & CJ2 \ CJ3 & CJ4 \ CJ5 & CJ6 \ ] = [ \partial c_1/ \partial x_1 & \... ... \partial x_2 \ \partial c_3/ \partial x_1 & \partial c_3/ \partial x_2 \ ] .$

The mc rows of the Jacobian matrix must be in the same order as the mc corresponding names of nonlinear constraints listed in the NLINCON statement. The n columns of the Jacobian matrix must be in the same order as the n corresponding parameter names listed in the DECVAR statement. To specify the values of nonzero derivatives, the variables specified in the JACOBIAN statement have to be defined on the left-hand side of algebraic expressions in programming statements.

For example,

  array cd[3,4] cd1-cd12;
  nlincon c1-c3 >= 0;
  jacnlc cd1-cd12;

  c1 = 8 - x1 * x1 - x2 * x2 - x3 * x3 - x4 * x4 -
         x1 + x2 - x3 + x4;
  c2 = 10 - x1 * x1 - 2 * x2 * x2 - x3 * x3 - 2 * x4 * x4 +
         x1 + x4;
  c3 = 5 - 2 * x1 * x2 - x2 * x2 - x3 * x3 - 2 * x1 + x2 + x4;

  cd[1,1]= -1 - 2 * x1;   cd[1,2]= 1 - 2 * x2;
  cd[1,3]= -1 - 2 * x3;   cd[1,4]= 1 - 2 * x4;
  cd[2,1]=  1 - 2 * x1;   cd[2,2]= -4 * x2;
  cd[2,3]= -2 * x3;       cd[2,4]= 1 - 4 * x4;
  cd[3,1]= -2 - 4 * x1;   cd[3,2]= 1 - 2 * x2;
  cd[3,3]= -2 * x3;       cd[3,4]= 1;

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