static void Main()
{
try {
// Create environment
GRBEnv env = new GRBEnv();
// Create a new m
GRBModel m = new GRBModel(env);
double lb = 0.0, ub = GRB.INFINITY;
GRBVar x = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x");
GRBVar y = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y");
GRBVar u = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "u");
GRBVar v = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "v");
// Set objective
m.SetObjective(2 * x + y, GRB.MAXIMIZE);
// Add linear constraint
m.AddConstr(u + 4 * v <= 9, "l1");
// Approach 1) PWL constraint approach
double intv = 1e-3;
double xmax = Math.Log(9.0);
int len = (int)Math.Ceiling(xmax / intv) + 1;
double[] xpts = new double[len];
double[] upts = new double[len];
for (int i = 0; i < len; i++)
{
xpts[i] = i * intv;
upts[i] = f(i * intv);
}
GRBGenConstr gc1 = m.AddGenConstrPWL(x, u, xpts, upts, "gc1");
double ymax = (9.0 / 4.0) * (9.0 / 4.0);
len = (int)Math.Ceiling(ymax / intv) + 1;
double[] ypts = new double[len];
double[] vpts = new double[len];
for (int i = 0; i < len; i++)
{
ypts[i] = i * intv;
vpts[i] = g(i * intv);
}
GRBGenConstr gc2 = m.AddGenConstrPWL(y, v, ypts, vpts, "gc2");
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Approach 2) General function constraint approach with auto PWL
// translation by Gurobi
// restore unsolved state and get rid of PWL constraints
m.Reset();
m.Remove(gc1);
m.Remove(gc2);
m.Update();
GRBGenConstr gcf1 = m.AddGenConstrExp(x, u, "gcf1", "");
GRBGenConstr gcf2 = m.AddGenConstrPow(y, v, 0.5, "gcf2", "");
m.Parameters.FuncPieceLength = 1e-3;
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Zoom in, use optimal solution to reduce the ranges and use a smaller
// pclen=1e-5 to solve it
x.LB = Math.Max(x.LB, x.X - 0.01);
x.UB = Math.Min(x.UB, x.X + 0.01);
y.LB = Math.Max(y.LB, y.X - 0.01);
y.UB = Math.Min(y.UB, y.X + 0.01);
m.Update();
m.Reset();
m.Parameters.FuncPieceLength = 1e-5;
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Dispose of model and environment
m.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
}
}