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### gc_pwl_c.c

/* Copyright 2020, 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)
*/

#include <stdlib.h>
#include <stdio.h>
#include "gurobi_c.h"

int
main(int argc,
char *argv[])
{
GRBenv   *env   = NULL;
GRBmodel *model = NULL;
int      *cbeg  = NULL;
int      *clen  = NULL;
int      *cind  = NULL;
double   *cval  = NULL;
double   *rhs   = NULL;
char     *sense = NULL;
double   *lb    = NULL;
double   *obj   = NULL;
int       nz, i, j;
int       status;
double    objval;
int       error = 0;

int n = 5;
int m = 5;
double c[] = { 0.5, 0.8, 0.5, 0.1, -1 };
double A[][5] = { {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} };
int npts = 5;
double xpts[] = {-1, 0, 0, 0, 1};
double ypts[] = {2, 1, 0, 1, 2};

/* Create environment */
if (error) goto QUIT;

/* Allocate memory and build the model */
nz = n; /* count nonzeros for n y variables */
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (A[i][j] != 0.0) nz++;
}
}

cbeg  = (int *) malloc(2*n*sizeof(int));
clen  = (int *) malloc(2*n*sizeof(int));
cind  = (int *) malloc(nz*sizeof(int));
cval  = (double *) malloc(nz*sizeof(double));
rhs   = (double *) malloc((m+1)*sizeof(double));
sense = (char *) malloc((m+1)*sizeof(char));
lb    = (double *) malloc(2*n*sizeof(double));
obj   = (double *) malloc(2*n*sizeof(double));

for (j = 0; j < n; j++) {
/* for x variables */
lb[j]  = -GRB_INFINITY;
obj[j] = c[j];
/* for y variables */
lb[j+n] = 0.0;
obj[j+n] = 0.0;
}

for (i = 0; i < m; i++) {
rhs[i] = 0.0;
sense[i] = GRB_LESS_EQUAL;
}
sense[m] = GRB_LESS_EQUAL;
rhs[m] = 3;

nz = 0;
for (j = 0; j < n; j++) {
cbeg[j] = nz;
for (i = 0; i < m; i++) {
if (A[i][j] != 0.0 ) {
cind[nz] = i;
cval[nz] = A[i][j];
nz++;
}
}
clen[j] = nz - cbeg[j];
}

for (j = 0; j < n; j++) {
cbeg[n+j] = nz;
clen[n+j] = 1;
cind[nz] = m;
cval[nz] = 1.0;
nz++;
}

error = GRBloadmodel(env, &model, "gc_pwl_c", 2*n, m+1,
GRB_MAXIMIZE, 0.0, obj, sense, rhs,
cbeg, clen, cind, cval, lb, NULL,
NULL, NULL, NULL);
if (error) goto QUIT;

for (j = 0; j < n; j++) {
error = GRBaddgenconstrPWL(model, NULL, j, n+j, npts, xpts, ypts);
if (error) goto QUIT;
}

/* Optimize model */
error = GRBoptimize(model);
if (error) goto QUIT;

for (j = 0; j < n; j++) {
double x;
error = GRBgetdblattrelement(model, "X", j, &x);
if (error) goto QUIT;
printf("x[%d] = %g\n", j, x);
}

/* Report the result */
error = GRBgetintattr(model, GRB_INT_ATTR_STATUS, &status);
if (error) goto QUIT;

if (status != GRB_OPTIMAL) {
fprintf(stderr, "Error: it isn't optimal\n");
goto QUIT;
}

error = GRBgetdblattr(model, GRB_DBL_ATTR_OBJVAL, &objval);
if (error) goto QUIT;
printf("Obj: %g\n", objval);

QUIT:

/* Error reporting */
if (error) {
printf("ERROR: %s\n", GRBgeterrormsg(env));
exit(1);
}

/* Free data */
if (cbeg)  free(cbeg);
if (clen)  free(clen);
if (cind)  free(cind);
if (cval)  free(cval);
if (rhs)   free(rhs);
if (sense) free(sense);
if (lb)    free(lb);
if (obj)   free(obj);

/* Free model */
GRBfreemodel(model);

/* Free environment */
GRBfreeenv(env);

return 0;
}


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