3.2.14 The QUADRATIC, HESSIAN, QUADS, QUADOBJ or QSECTION Data Cards

The QUADRACTIC, HESSIAN, QUADS¹, QUADOBJ²and QSECTION³indicator cards are used interchangeably to announce any nonzero coefficients ${h_{j,k}}$ in the quadratic objective group ${{\scriptstyle \frac{1}{2}}\sum_{j=1}^n \sum_{k=1}^n h_{j,k} x_j x_k }$. Only one of each pair ${(h_{j,k}, h_{k,j})}$, ${(j \neq k)}$, of ``off-diagonal'' terms should be given, but which is unimportant. Any repeated coefficients will be summed. The syntax for data following these indicator cards is given in Figure 3.15.

Figure 3.15: Possible data cards for HESSIAN, QUADS, QUADOBJ or QSECTION

The strings varbl-name in data fields 2 and 3 (and optionally 2 and 5 for those cards whose field 1 does not contain Z) give the names of pairs of problem variables ${x_j}$ and ${x_k}$ for which ${h_{j,k}}$ is nonzero. All problem variables must have been previously set in the VARIABLES/COLUMNS section. Additionally, on a Z card, the name of the variable must be an element of an array of variables, with a valid name and index, while on a X card, the name may be either a scalar or an array name.

On cards whose field 1 is either empty or contains the character X, the strings numerical-vl in data fields 4 and (optionally) 6 contain the associated numerical values of the coefficients ${h_{j,k}}$. On cards for which field 1 contains the character Z, the string r-p-a-name in data field 5 gives a real parameter array name. This name must have been previously defined and its associated value then gives the numerical value of the parameter.