In Section 2.4, we gave a second example. Because of its repetitious structure, this example is well suited to use array names and do-loops. An SDIF file for this example is given in Figure 3.22. The problem is given the name DOC2. The variables are referred to as X1,..., X1000 and the groups are G1, ..., G1000. The vector of bounds is called BND, the constants are CONST and the single nonlinear element type is SQUARE, with elemental variable V. Note that the BND section is necessary since the variables are unrestricted and we must override the default lower bounds of zero and upper bounds of infinity. The nonlinear elements are given the names E1,..., E1000. Finally, the single group type is SINE with group-type variable ALPHA and parameter P.