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## Cloud Guide

Piecewise.java

### Piecewise.java

```/* Copyright 2018, Gurobi Optimization, LLC */

/* This example considers the following separable, convex problem:

minimize    f(x) - y + g(z)
subject to  x + 2 y + 3 z <= 4
x +   y       >= 1
x,    y,    z <= 1

where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It
formulates and solves a simpler LP model by approximating f and
g with piecewise-linear functions. Then it transforms the model
into a MIP by negating the approximation for f, which corresponds
to a non-convex piecewise-linear function, and solves it again.
*/

import gurobi.*;

public class Piecewise {

private static double f(double u) { return Math.exp(-u); }
private static double g(double u) { return 2 * u * u - 4 * u; }

public static void main(String[] args) {
try {

// Create environment

GRBEnv env = new GRBEnv();

// Create a new model

GRBModel model = new GRBModel(env);

// Create variables

double lb = 0.0, ub = 1.0;

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

// Set objective for y

GRBLinExpr obj = new GRBLinExpr();
model.setObjective(obj);

// Add piecewise-linear objective functions for x and z

int npts = 101;
double[] ptu = new double[npts];
double[] ptf = new double[npts];
double[] ptg = new double[npts];

for (int i = 0; i < npts; i++) {
ptu[i] = lb + (ub - lb) * i / (npts - 1);
ptf[i] = f(ptu[i]);
ptg[i] = g(ptu[i]);
}

model.setPWLObj(x, ptu, ptf);
model.setPWLObj(z, ptu, ptg);

// Add constraint: x + 2 y + 3 z <= 4

GRBLinExpr expr = new GRBLinExpr();

// Add constraint: x + y >= 1

expr = new GRBLinExpr();

// Optimize model as an LP

model.optimize();

System.out.println("IsMIP: " + model.get(GRB.IntAttr.IsMIP));

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));

System.out.println();

// Negate piecewise-linear objective function for x

for (int i = 0; i < npts; i++) {
ptf[i] = -ptf[i];
}

model.setPWLObj(x, ptu, ptf);

// Optimize model as a MIP

model.optimize();

System.out.println("IsMIP: " + model.get(GRB.IntAttr.IsMIP));

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));

// Dispose of model and environment

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

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