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### gc_pwl_cs.cs

/* Copyright 2023, Gurobi Optimization, LLC

This example formulates and solves the following simple model
with PWL constraints:

maximize
sum c[j] * x[j]
subject to
sum A[i,j] * x[j] <= 0,  for i = 0, ..., m-1
sum y[j] <= 3
y[j] = pwl(x[j]),        for j = 0, ..., n-1
x[j] free, y[j] >= 0,    for j = 0, ..., n-1
where pwl(x) = 0,     if x  = 0
= 1+|x|, if x != 0

Note
1. sum pwl(x[j]) <= b is to bound x vector and also to favor sparse x vector.
Here b = 3 means that at most two x[j] can be nonzero and if two, then
sum x[j] <= 1
2. pwl(x) jumps from 1 to 0 and from 0 to 1, if x moves from negative 0 to 0,
then to positive 0, so we need three points at x = 0. x has infinite bounds
on both sides, the piece defined with two points (-1, 2) and (0, 1) can
extend x to -infinite. Overall we can use five points (-1, 2), (0, 1),
(0, 0), (0, 1) and (1, 2) to define y = pwl(x)
*/

using System;
using Gurobi;

public class gc_pwl_cs {

public static void Main() {
try {
int n = 5;
int m = 5;
double[] c = new double[] { 0.5, 0.8, 0.5, 0.1, -1 };
double[,] A = new double[,] { {0, 0, 0, 1, -1},
{0, 0, 1, 1, -1},
{1, 1, 0, 0, -1},
{1, 0, 1, 0, -1},
{1, 0, 0, 1, -1} };
double[] xpts = new double[] {-1, 0, 0, 0, 1};
double[] ypts = new double[] {2, 1, 0, 1, 2};

// Env and model
GRBEnv env = new GRBEnv();
GRBModel model = new GRBModel(env);
model.ModelName = "gc_pwl_cs";

// Add variables, set bounds and obj coefficients
for (int i = 0; i < n; i++) {
x[i].LB = -GRB.INFINITY;
x[i].Obj = c[i];
}

// Set objective to maximize
model.ModelSense = GRB.MAXIMIZE;

for (int i = 0; i < m; i++) {
GRBLinExpr le = 0.0;
for (int j = 0; j < n; j++) {
}
model.AddConstr(le, GRB.LESS_EQUAL, 0, "cx" + i);
}

GRBLinExpr le1 = 0.0;
for (int j = 0; j < n; j++) {
}

for (int j = 0; j < n; j++) {
model.AddGenConstrPWL(x[j], y[j], xpts, ypts, "pwl" + j);
}

// Optimize model
model.Optimize();

for (int j = 0; j < n; j++) {
Console.WriteLine("x[" + j + "] = " + x[j].X);
}
Console.WriteLine("Obj: " + model.ObjVal);

// Dispose of model and environment
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
}
}
}


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