Optimization problems.

In algebraic optimization problems one must set ICP(1)=10, as AUTO uses PAR(10) as principal continuation parameter to monitor the value of the objective function. Furthermore, one must designate one free equation parameter in ICP(2). Thus, NICP=2 in the first run.

Folds with respect to PAR(10) correspond to extrema of the objective function. In a second run one can restart at such a fold, with an additional free equation parameter specified in ICP(3). Thus, NICP=3 in the second run.

The above procedure can be repeated. For example, folds from the second run can be continued in a third run with three equation parameters specified in addition to PAR(10). Thus, NICP=4 in the third run.

For a simple example see demo opt, where a four-parameter extremum is located. Note that NICP=5 in each of the four constants-files of this demo, with the indices of PAR(10) and PAR(1)-PAR(4) specified in ICP. Thus, in the first three runs, there are overspecified parameters. However, AUTO will always use the correct number of parameters. Although the overspecified parameters will be printed, their values will remain fixed.