int QSopt_dual (QSprob p, int *status)

The dual simplex algorithm is the method of choice for many forms of LP problems when solving the problem from scratch. The algorithm is also an effective solution procedure for re-optimizing problems after the addition of constraints (adding constraints keeps the current dual solution feasible).

After a call to QSopt_dual, the status variable should be checked to determine the status of the solution. In the most common cases, either an optimal solution is found (indicated by a value of QS_LP_OPTIMAL), or the problem is shown to be in infeasible (QS_LP_INFEASIBLE), or the problem is shown to be unbounded (QS_LP_UNBOUNDED). Optimization Status Codes gives a full list of the possible values for status.

By default QSopt_dual will solve the specified LP problem using the dual steepest-edge pricing rule. This rule is effective for many difficult LP problems, but for problems that are relatively easy to solve (even though they may be very large in size) a less time-consuming pricing rule may be preferable. To select an alternative pricing rule, the QSset_param function can be used with the whichparam argument set to the value given below.

	Constant		Parameter
	QS_PARAM_DUAL_PRICING		Dual Pricing

The QSopt library has available three pricing rules for the dual simplex algorithm. The pricing rule can be specified in QSset_param by setting the newvalue argument to one of the values given below.

	Constant		Rule
	QS_PRICE_DDANTZIG		Dual Dantzig
	QS_PRICE_DSTEEP		Dual steepest-edge
	QS_PRICE_DMULTPARTIAL		Dual multiple-partial

See Parameter Setting for the Optimizer for more parameters associated with the optimization algorithm

int status, rval;

/* p is a QSprob, a handle to an existing LP problem */

rval = QSopt_dual (p, &status);
if (rval) {
    fprintf (stderr, "QSopt_dual failed with return code %d\n", rval);
} else {
    switch (status) {
    case QS_LP_OPTIMAL:
        printf ("Found optimal solution to LP\n");
        break;
    case QS_LP_INFEASIBLE:
        printf ("No feasible solution exists for the LP\n");
        break;
    case QS_LP_UNBOUNDED:
        printf ("The LP objective is unbounded\n");
        break;
    default:
        printf ("LP could not be solved, status = %d\n", status);
        break;
    }
}