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### Bilinear.java

/* Copyright 2023, Gurobi Optimization, LLC */

/* This example formulates and solves the following simple bilinear model:

maximize    x
subject to  x + y + z <= 10
x * y <= 2          (bilinear inequality)
x * z + y * z == 1  (bilinear equality)
x, y, z non-negative (x integral in second version)
*/

import gurobi.*;

public class Bilinear {
public static void main(String[] args) {
try {
GRBEnv    env   = new GRBEnv("bilinear.log");
GRBModel  model = new GRBModel(env);

// Create variables

GRBVar x = model.addVar(0.0, GRB.INFINITY, 0.0, GRB.CONTINUOUS, "x");
GRBVar y = model.addVar(0.0, GRB.INFINITY, 0.0, GRB.CONTINUOUS, "y");
GRBVar z = model.addVar(0.0, GRB.INFINITY, 0.0, GRB.CONTINUOUS, "z");

// Set objective

GRBLinExpr obj = new GRBLinExpr();
obj.addTerm(1.0, x);
model.setObjective(obj, GRB.MAXIMIZE);

// Add linear constraint: x + y + z <= 10

GRBLinExpr expr = new GRBLinExpr();
expr.addTerm(1.0, x); expr.addTerm(1.0, y); expr.addTerm(1.0, z);
model.addConstr(expr, GRB.LESS_EQUAL, 10.0, "c0");

// Add bilinear inequality: x * y <= 2

GRBQuadExpr qexpr = new GRBQuadExpr();
qexpr.addTerm(1.0, x, y);
model.addQConstr(qexpr, GRB.LESS_EQUAL, 2.0, "bilinear0");

// Add bilinear equality: x * z + y * z == 1

qexpr = new GRBQuadExpr();
qexpr.addTerm(1.0, x, z);
qexpr.addTerm(1.0, y, z);
model.addQConstr(qexpr, GRB.EQUAL, 1.0, "bilinear1");

// First optimize() call will fail - need to set NonConvex to 2

try {
model.optimize();
assert false;
} catch (GRBException e) {
System.out.println("Failed (as expected)");
}

// Change parameter and optimize again

model.set(GRB.IntParam.NonConvex, 2);
model.optimize();

System.out.println(x.get(GRB.StringAttr.VarName)
+ " " +x.get(GRB.DoubleAttr.X));
System.out.println(y.get(GRB.StringAttr.VarName)
+ " " +y.get(GRB.DoubleAttr.X));
System.out.println(z.get(GRB.StringAttr.VarName)
+ " " +z.get(GRB.DoubleAttr.X));

System.out.println("Obj: " + model.get(GRB.DoubleAttr.ObjVal) + " " +
obj.getValue());
System.out.println();

// Constrain x to be integral and solve again

x.set(GRB.CharAttr.VType, GRB.INTEGER);
model.optimize();

System.out.println(x.get(GRB.StringAttr.VarName)
+ " " +x.get(GRB.DoubleAttr.X));
System.out.println(y.get(GRB.StringAttr.VarName)
+ " " +y.get(GRB.DoubleAttr.X));
System.out.println(z.get(GRB.StringAttr.VarName)
+ " " +z.get(GRB.DoubleAttr.X));

System.out.println("Obj: " + model.get(GRB.DoubleAttr.ObjVal) + " " +
obj.getValue());
System.out.println();

// Dispose of model and environment

model.dispose();
env.dispose();

} catch (GRBException e) {
System.out.println("Error code: " + e.getErrorCode() + ". " +
e.getMessage());
}
}
}


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