The routine CPXfeasoptext extends CPXfeasopt in several ways. Unlike CPXfeasopt, CPXfeasoptext enables the user to relax quadratic constraints and indicator constraints. In addition, it allows the user to treat a group of constraints as a single constraint for the purposes of determining the penalty for relaxation.

Thus, according to the various INF relaxation penalty metrics (see CPXfeasopt for a list of the available metrics), all constraints in a group can be relaxed for a penalty of one unit. Similarly, according to the various QUAD metrics, the penalty of relaxing a group grows as the square of the sum of the individual member relaxations, rather than as the sum of the squares of the individual relaxations.

Note that if you use INF mode, the resulting feasopt models will be MIPs even if your model is continuous. Similarly, if you use QUAD mode, the feasopt models will become quadratic even if your original model is linear. This difference can result in greater than expected solve times.

The routine also computes a relaxed solution vector that can be queried with CPXsolution, CPXgetcolinfeas for columns, CPXgetrowinfeas for rows, CPXgetqconstrinfeas for quadratic constraints, CPXgetindconstrinfeas for indicator constraints, or CPXgetsosinfeas for special ordered sets.

The arguments to this routine define the set of groups, Each group contains a list of member constraints, and each member has a type (lower bound, upper bound, linear constraint, quadratic constraint, or indicator constraint). The group members and member types are entered by means of a data structure similar to the sparse matrix data structure used throughout CPLEX. (See CPXcopylp for one example.) The argument grpbeg gives the starting location of each group in grpind and grptype. The list of members for group i can be found in grpind[grpbeg[i]] through grpind[grpbeg[i+1]-1], for i less than grpcnt-1 and grpind[grpbeg[i]] through grpind[concnt-1] for i = grpcnt-1. The corresponding constraint types for these members can be found in grptype[grpbeg[i]] through grptype[grpbeg[i+1]-1], for i less than concnt-1 and grptype[grpbeg[grpcnt-1]] through grptype[concnt-1] for i = grpcnt-1. A constraint can appear in at most one group. A constraint that appears in no group will not be relaxed.