分段_C.C.
/ * 2021年版权,Gurobi优狗万app足彩化,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. */ #include #include #include #include "gurobi_c.h" double f(double u) { return exp(-u); } double g(double u) { return 2 * u * u - 4 * u; } int main(int argc, char *argv[]) { GRBenv *env = NULL; GRBmodel *model = NULL; int error = 0; double lb, ub; int npts, i; double *ptu = NULL; double *ptf = NULL; double *ptg = NULL; int ind[3]; double val[3]; int ismip; double objval; double sol[3]; /* Create environment */ error = GRBloadenv(&env, NULL); if (error) goto QUIT; /* Create a new model */ error = GRBnewmodel(env, &model, NULL, 0, NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT; /* Add variables */ lb = 0.0; ub = 1.0; error = GRBaddvar(model, 0, NULL, NULL, 0.0, lb, ub, GRB_CONTINUOUS, "x"); if (error) goto QUIT; error = GRBaddvar(model, 0, NULL, NULL, 0.0, lb, ub, GRB_CONTINUOUS, "y"); if (error) goto QUIT; error = GRBaddvar(model, 0, NULL, NULL, 0.0, lb, ub, GRB_CONTINUOUS, "z"); if (error) goto QUIT; /* Set objective for y */ error = GRBsetdblattrelement(model, GRB_DBL_ATTR_OBJ, 1, -1.0); if (error) goto QUIT; /* Add piecewise-linear objective functions for x and z */ npts = 101; ptu = (double *) malloc(npts * sizeof(double)); ptf = (double *) malloc(npts * sizeof(double)); ptg = (double *) malloc(npts * sizeof(double)); for (i = 0; i < npts; i++) { ptu[i] = lb + (ub - lb) * i / (npts - 1); ptf[i] = f(ptu[i]); ptg[i] = g(ptu[i]); } error = GRBsetpwlobj(model, 0, npts, ptu, ptf); if (error) goto QUIT; error = GRBsetpwlobj(model, 2, npts, ptu, ptg); if (error) goto QUIT; /* Add constraint: x + 2 y + 3 z <= 4 */ ind[0] = 0; ind[1] = 1; ind[2] = 2; val[0] = 1; val[1] = 2; val[2] = 3; error = GRBaddconstr(model, 3, ind, val, GRB_LESS_EQUAL, 4.0, "c0"); if (error) goto QUIT; /* Add constraint: x + y >= 1 */ ind[0] = 0; ind[1] = 1; val[0] = 1; val[1] = 1; error = GRBaddconstr(model, 2, ind, val, GRB_GREATER_EQUAL, 1.0, "c1"); if (error) goto QUIT; /* Optimize model as an LP */ error = GRBoptimize(model); if (error) goto QUIT; error = GRBgetintattr(model, "IsMIP", &ismip); if (error) goto QUIT; error = GRBgetdblattr(model, "ObjVal", &objval); if (error) goto QUIT; error = GRBgetdblattrarray(model, "X", 0, 3, sol); if (error) goto QUIT; printf("IsMIP: %d\n", ismip); printf("x %g\ny %g\nz %g\n", sol[0], sol[1], sol[2]); printf("Obj: %g\n", objval); printf("\n"); /* Negate piecewise-linear objective function for x */ for (i = 0; i < npts; i++) { ptf[i] = -ptf[i]; } error = GRBsetpwlobj(model, 0, npts, ptu, ptf); if (error) goto QUIT; /* Optimize model as a MIP */ error = GRBoptimize(model); if (error) goto QUIT; error = GRBgetintattr(model, "IsMIP", &ismip); if (error) goto QUIT; error = GRBgetdblattr(model, "ObjVal", &objval); if (error) goto QUIT; error = GRBgetdblattrarray(model, "X", 0, 3, sol); if (error) goto QUIT; printf("IsMIP: %d\n", ismip); printf("x %g\ny %g\nz %g\n", sol[0], sol[1], sol[2]); printf("Obj: %g\n", objval); QUIT: /* Error reporting */ if (error) { printf("ERROR: %s\n", GRBgeterrormsg(env)); exit(1); } /* Free data */ free(ptu); free(ptf); free(ptg); /* Free model */ GRBfreemodel(model); /* Free environment */ GRBfreeenv(env); return 0; }
