public static void Main(string[] args)
{
try {
Cplex cplex = new Cplex();
ILPMatrix lp = PopulateByRow(cplex);
int[] ind = { 0 };
double[] val = { 1.0 };
// When a non-convex objective function is present, CPLEX
// will raise an exception unless the parameter
// Cplex.Param.SolutionTarget is set to accept
// first-order optimal solutions
cplex.SetParam(Cplex.Param.SolutionTarget, 2);
// CPLEX may converge to either local optimum
SolveAndDisplay(cplex, lp);
// Add a constraint that cuts off the solution at (-1, 1)
lp.AddRow(0.0, System.Double.MaxValue, ind, val);
SolveAndDisplay(cplex, lp);
// Remove the newly added constraint and add a new constraint
// with the opposite sense to cut off the solution at (1, 1)
lp.RemoveRow(lp.Nrows - 1);
lp.AddRow(-System.Double.MaxValue, 0.0, ind, val);
SolveAndDisplay(cplex, lp);
cplex.ExportModel("indefqpex1.lp");
cplex.End();
}
catch (ILOG.Concert.Exception e) {
System.Console.WriteLine("Concert exception '" + e + "' caught");
}
}
static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, Double.MaxValue, Double.MaxValue };
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
INumVar y = model.IntVar(model.Column(lp), 0, 3);
// - x0 + x1 + x2 + 10*y <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = { -Double.MaxValue, -Double.MaxValue };
double[] rhs = { 20.0, 30.0 };
double[][] val = { new double[] { -1.0, 1.0, 1.0, 10.0 },
new double[] { 1.0, -3.0, 1.0 } };
int[][] ind = { new int[] { 0, 1, 2, 3 },
new int[] { 0, 1, 2 } };
lp.AddRows(lhs, rhs, ind, val);
// x1 + 3.5*y = 0
lp.AddRow(model.Eq(model.Diff(x[1], model.Prod(3.5, y)), 0.0));
// Q = 0.5 ( 33*x0*x0 + 22*x1*x1 + 11*x2*x2 - 12*x0*x1 - 23*x1*x2 )
INumExpr x00 = model.Prod(33.0, model.Square(x[0]));
INumExpr x11 = model.Prod(22.0, model.Square(x[1]));
INumExpr x22 = model.Prod(11.0, model.Square(x[2]));
INumExpr x01 = model.Prod(-12.0, model.Prod(x[0], x[1]));
INumExpr x12 = model.Prod(-23.0, model.Prod(x[1], x[2]));
INumExpr Q = model.Prod(0.5, model.Sum(x00, x11, x22, x01, x12));
// maximize x0 + 2*x1 + 3*x2 + Q
double[] objvals = { 1.0, 2.0, 3.0 };
model.Add(model.Maximize(model.Diff(model.ScalProd(x, objvals), Q)));
return(lp);
}