internal static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, System.Double.MaxValue, System.Double.MaxValue };
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = { -System.Double.MaxValue, -System.Double.MaxValue };
double[] rhs = { 20.0, 30.0 };
double[][] val = { new double[] { -1.0, 1.0, 1.0 },
new double[] { 1.0, -3.0, 1.0 } };
int[][] ind = { new int[] { 0, 1, 2 },
new int[] { 0, 1, 2 } };
lp.AddRows(lhs, rhs, ind, val);
// 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);
}
internal static INumVar[] populateByRow(IMPModeler model,
IRange[] row)
{
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, System.Double.MaxValue, System.Double.MaxValue };
INumVar[] x = model.NumVarArray(3, lb, ub);
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[][] val = { new double[] { -1.0, 1.0, 1.0 },
new double[] { 1.0, -3.0, 1.0 } };
row[0] = model.AddLe(model.ScalProd(val[0], x), 20.0);
row[1] = model.AddLe(model.ScalProd(val[1], x), 30.0);
// x0*x0 + x1*x1 + x2*x2 <= 1.0
row[2] = model.AddLe(model.Sum(model.Prod(x[0], x[0]),
model.Prod(x[1], x[1]),
model.Prod(x[2], x[2])), 1.0);
// Q = 0.5 ( 33*x0*x0 + 22*x1*x1 + 11*x2*x2 - 12*x0*x1 - 23*x1*x2 )
INumExpr x00 = model.Prod(33.0, x[0], x[0]);
INumExpr x11 = model.Prod(22.0, x[1], x[1]);
INumExpr x22 = model.Prod(11.0, x[2], x[2]);
INumExpr x01 = model.Prod(-12.0, x[0], x[1]);
INumExpr x12 = model.Prod(-23.0, 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(x);
}
// To populate by row, we first create the variables, and then use them to
// create the range constraints and objective. The model we create is:
//
// Minimize
// obj: - 0.5 (-3 * xˆ2 - 3 * yˆ2 - 1 * x * y)
// Subject To
// c1: -x + y >= 0
// c2: x + y >= 0
// Bounds
// -1 <= x <= 1
// 0 <= y <= 1
// End
internal static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = { -1.0, 0.0 };
double[] ub = { 1.0, 1.0 };
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 2), lb, ub);
double[] lhs = { 0.0, 0.0 };
double[] rhs = { System.Double.MaxValue, System.Double.MaxValue };
double[][] val = { new double[] { -1.0, 1.0 },
new double[] { 1.0, 1.0 } };
int[][] ind = { new int[] { 0, 1 },
new int[] { 0, 1 } };
lp.AddRows(lhs, rhs, ind, val);
INumExpr x00 = model.Prod(-3.0, x[0], x[0]);
INumExpr x11 = model.Prod(-3.0, x[1], x[1]);
INumExpr x01 = model.Prod(-1.0, x[0], x[1]);
INumExpr Q = model.Prod(0.5, model.Sum(x00, x11, x01));
model.Add(model.Minimize(Q));
return(lp);
}
internal static void PopulateByNonzero(IMPModeler model,
INumVar[][] var,
IRange[][] rng)
{
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, System.Double.MaxValue, System.Double.MaxValue };
INumVar[] x = model.NumVarArray(3, lb, ub);
var[0] = x;
double[] objvals = { 1.0, 2.0, 3.0 };
model.Add(model.Maximize(model.ScalProd(x, objvals)));
rng[0] = new IRange[2];
rng[0][0] = model.AddRange(-System.Double.MaxValue, 20.0);
rng[0][1] = model.AddRange(-System.Double.MaxValue, 30.0);
rng[0][0].Expr = model.Sum(model.Prod(-1.0, x[0]),
model.Prod(1.0, x[1]),
model.Prod(1.0, x[2]));
rng[0][1].Expr = model.Sum(model.Prod(1.0, x[0]),
model.Prod(-3.0, x[1]),
model.Prod(1.0, x[2]));
x[0].Name = "x1";
x[1].Name = "x2";
x[2].Name = "x3";
rng[0][0].Name = "c1";
rng[0][0].Name = "c2";
}
// Creating a simple QP problem
internal static ILPMatrix CreateQPModel(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = { 0.0, 0.0, 0.0 };
double[] ub = { 40.0, System.Double.MaxValue, System.Double.MaxValue };
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
int nvars = x.Length;
for (int j = 0; j < nvars; ++j)
{
x[j].Name = "x" + j;
}
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = { -System.Double.MaxValue, -System.Double.MaxValue };
double[] rhs = { 20.0, 30.0 };
double[][] val = { new double[] { -1.0, 1.0, 1.0 },
new double[] { 1.0, -3.0, 1.0 } };
int[][] ind = { new int[] { 0, 1, 2 },
new int[] { 0, 1, 2 } };
lp.AddRows(lhs, rhs, ind, val);
// minimize - x0 - x1 - x2 + x0*x0 + x1*x1 + x0*x1 + x1*x0
ILQNumExpr objExpr = model.LqNumExpr();
for (int i = 0; i < nvars; ++i)
{
objExpr.AddTerm(-1.0, x[i]);
for (int j = 0; j < nvars; ++j)
{
objExpr.AddTerm(1.0, x[i], x[j]);
}
}
IObjective obj = model.Minimize(objExpr);
model.Add(obj);
// Print out the objective function
PrintObjective(obj);
return(lp);
}
// Creating a simple QP problem
internal static ILPMatrix CreateQPModel(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
int nvars = x.Length;
for (int j = 0; j < nvars; ++j)
x[j].Name = "x" +j;
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = { -System.Double.MaxValue, -System.Double.MaxValue };
double[] rhs = { 20.0, 30.0 };
double[][] val = { new double[] {-1.0, 1.0, 1.0},
new double[] { 1.0, -3.0, 1.0} };
int[][] ind = { new int[] {0, 1, 2},
new int[] {0, 1, 2} };
lp.AddRows(lhs, rhs, ind, val);
// minimize - x0 - x1 - x2 + x0*x0 + x1*x1 + x0*x1 + x1*x0
ILQNumExpr objExpr = model.LqNumExpr();
for (int i = 0; i < nvars; ++i) {
objExpr.AddTerm(-1.0, x[i]);
for (int j = 0; j < nvars; ++j) {
objExpr.AddTerm(1.0, x[i], x[j]);
}
}
IObjective obj = model.Minimize(objExpr);
model.Add(obj);
// Print out the objective function
PrintObjective(obj);
return lp;
}
internal static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 3), lb, ub);
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[] lhs = {-System.Double.MaxValue, -System.Double.MaxValue};
double[] rhs = {20.0, 30.0};
double[][] val = { new double[] {-1.0, 1.0, 1.0},
new double[] { 1.0, -3.0, 1.0} };
int[][] ind = { new int[] {0, 1, 2},
new int[] {0, 1, 2} };
lp.AddRows(lhs, rhs, ind, val);
// 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);
}
// To populate by row, we first create the variables, and then use them to
// create the range constraints and objective. The model we create is:
//
// Minimize
// obj: - 0.5 (-3 * xˆ2 - 3 * yˆ2 - 1 * x * y)
// Subject To
// c1: -x + y >= 0
// c2: x + y >= 0
// Bounds
// -1 <= x <= 1
// 0 <= y <= 1
// End
internal static ILPMatrix PopulateByRow(IMPModeler model)
{
ILPMatrix lp = model.AddLPMatrix();
double[] lb = {-1.0, 0.0};
double[] ub = { 1.0, 1.0};
INumVar[] x = model.NumVarArray(model.ColumnArray(lp, 2), lb, ub);
double[] lhs = {0.0, 0.0};
double[] rhs = {System.Double.MaxValue, System.Double.MaxValue};
double[][] val = {new double[] {-1.0, 1.0},
new double[] { 1.0, 1.0}};
int[][] ind = {new int[] {0, 1},
new int[] {0, 1}};
lp.AddRows(lhs, rhs, ind, val);
INumExpr x00 = model.Prod(-3.0, x[0], x[0]);
INumExpr x11 = model.Prod(-3.0, x[1], x[1]);
INumExpr x01 = model.Prod(-1.0, x[0], x[1]);
INumExpr Q = model.Prod(0.5, model.Sum(x00, x11, x01));
model.Add(model.Minimize(Q));
return (lp);
}
internal static void PopulateByNonzero(IMPModeler model,
INumVar[][] var,
IRange[][] rng) {
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
INumVar[] x = model.NumVarArray(3, lb, ub);
var[0] = x;
double[] objvals = {1.0, 2.0, 3.0};
model.Add(model.Maximize(model.ScalProd(x, objvals)));
rng[0] = new IRange[2];
rng[0][0] = model.AddRange(-System.Double.MaxValue, 20.0);
rng[0][1] = model.AddRange(-System.Double.MaxValue, 30.0);
rng[0][0].Expr = model.Sum(model.Prod(-1.0, x[0]),
model.Prod( 1.0, x[1]),
model.Prod( 1.0, x[2]));
rng[0][1].Expr = model.Sum(model.Prod( 1.0, x[0]),
model.Prod(-3.0, x[1]),
model.Prod( 1.0, x[2]));
x[0].Name = "x1";
x[1].Name = "x2";
x[2].Name = "x3";
rng[0][0].Name = "c1";
rng[0][0].Name = "c2";
}
internal static INumVar[] populateByRow(IMPModeler model,
IRange[] row)
{
double[] lb = {0.0, 0.0, 0.0};
double[] ub = {40.0, System.Double.MaxValue, System.Double.MaxValue};
INumVar[] x = model.NumVarArray(3, lb, ub);
// - x0 + x1 + x2 <= 20
// x0 - 3*x1 + x2 <= 30
double[][] val = {new double[]{-1.0, 1.0, 1.0},
new double[]{ 1.0, -3.0, 1.0}};
row[0] = model.AddLe(model.ScalProd(val[0], x), 20.0);
row[1] = model.AddLe(model.ScalProd(val[1], x), 30.0);
// x0*x0 + x1*x1 + x2*x2 <= 1.0
row[2] = model.AddLe(model.Sum(model.Prod(x[0], x[0]),
model.Prod(x[1], x[1]),
model.Prod(x[2], x[2])), 1.0);
// Q = 0.5 ( 33*x0*x0 + 22*x1*x1 + 11*x2*x2 - 12*x0*x1 - 23*x1*x2 )
INumExpr x00 = model.Prod( 33.0, x[0], x[0]);
INumExpr x11 = model.Prod( 22.0, x[1], x[1]);
INumExpr x22 = model.Prod( 11.0, x[2], x[2]);
INumExpr x01 = model.Prod(-12.0, x[0], x[1]);
INumExpr x12 = model.Prod(-23.0, 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 x;
}