分段_cs.cs.
/ *版权所有2021，gurobi优狗万app足彩化，llc * // *该示例考虑以下可分离凸面问题：将F（x） - y + g（z）最小化为x + 2 y + 3 z <= 4 x + y> = 1 x，y，z <= 1其中f（u）= exp（-u）和g（u）= 2 u ^ 2 - 4 u，对于所有真实的u。通过近似F和G具有分段 - 线性函数来制定和解决简单的LP模型。然后，它通过否定F的近似来将模型转换为MIP，这对应于非凸分段线性函数，并再次解决。* /使用系统;使用gurobi;类分段_cs {私有静态双f（双u）{return math.exp（-u）;私人静态双g（双U）{返回2 * U * U - 4 * U;}静态void main（）{try {//创建环境grbenv ent = new grbenv（）;//创建一个新的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 model.SetObjective(-y); // 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 model.AddConstr(x + 2 * y + 3 * z <= 4.0, "c0"); // Add constraint: x + y >= 1 model.AddConstr(x + y >= 1.0, "c1"); // Optimize model as an LP model.Optimize(); Console.WriteLine("IsMIP: " + model.IsMIP); Console.WriteLine(x.VarName + " " + x.X); Console.WriteLine(y.VarName + " " + y.X); Console.WriteLine(z.VarName + " " + z.X); Console.WriteLine("Obj: " + model.ObjVal); Console.WriteLine(); // 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(); Console.WriteLine("IsMIP: " + model.IsMIP); Console.WriteLine(x.VarName + " " + x.X); Console.WriteLine(y.VarName + " " + y.X); Console.WriteLine(z.VarName + " " + z.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); } } }
