gc_pwl_c.c
/* 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) */ #include #include #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 */ error = GRBloadenv(&env, NULL); 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; /* Add piecewise constraints */ 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; }
