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### Qcp.java

/* Copyright 2022, Gurobi Optimization, LLC */

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

maximize    x
subject to  x + y + z = 1
x^2 + y^2 <= z^2 (second-order cone)
x^2 <= yz        (rotated second-order cone)
x, y, z non-negative
*/

import gurobi.*;

public class Qcp {
public static void main(String[] args) {
try {
GRBEnv    env   = new GRBEnv("qcp.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();
model.setObjective(obj, GRB.MAXIMIZE);

// Add linear constraint: x + y + z = 1

GRBLinExpr expr = new GRBLinExpr();
model.addConstr(expr, GRB.EQUAL, 1.0, "c0");

// Add second-order cone: x^2 + y^2 <= z^2

model.addQConstr(qexpr, GRB.LESS_EQUAL, 0.0, "qc0");

// Add rotated cone: x^2 <= yz

qexpr = new GRBQuadExpr();
model.addQConstr(qexpr, GRB.LESS_EQUAL, 0.0, "qc1");

// Optimize model

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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