/* File : portfolio_4_transcost.cs Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved. Description : Implements a basic portfolio optimization model with fixed setup costs and transaction costs as a mixed-integer problem. */ using System; namespace mosek.example { class msgclass : mosek.Stream { string prefix; public msgclass (string prfx) { prefix = prfx; } public override void streamCB (string msg) { Console.Write ("{0}{1}", prefix, msg); } } public class portfolio_4_transcost { public static void Main (String[] args) { // Since the value infinity is never used, we define // 'infinity' symbolic purposes only double infinity = 0; int n = 8; double[] mu = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379}; double[,] GT = { {0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638}, {0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506}, {0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914}, {0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742}, {0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 }, {0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 } }; int k = GT.GetLength(0); double[] x0 = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}; double w = 1.0; double gamma = 0.36; double totalBudget; double[] f = new double[n]; double[] g = new double[n]; for (int i = 0; i < n; ++i) { f[i] = 0.01; g[i] = 0.001; } // Offset of variables. int numvar = 3 * n; int voff_x = 0; int voff_z = n; int voff_y = 2 * n; // Offset of constraints. int numcon = 3 * n + 1; int coff_bud = 0; int coff_abs1 = 1; int coff_abs2 = 1 + n; int coff_swi = 1 + 2 * n; // Create a task object. using (mosek.Task task = new mosek.Task()) { // Directs the log task stream to the user specified // method msgclass.streamCB task.set_Stream(mosek.streamtype.log, new msgclass("")); // Variables (vector of x, z, y) task.appendvars(numvar); for (int j = 0; j < n; ++j) { /* Optionally we can give the variables names */ task.putvarname(voff_x + j, "x[" + (j + 1) + "]"); task.putvarname(voff_z + j, "z[" + (j + 1) + "]"); task.putvarname(voff_y + j, "y[" + (j + 1) + "]"); /* Apply variable bounds (x >= 0, z free, y binary) */ task.putvarbound(voff_x + j, mosek.boundkey.lo, 0.0, infinity); task.putvarbound(voff_z + j, mosek.boundkey.fr, -infinity, infinity); task.putvarbound(voff_y + j, mosek.boundkey.ra, 0.0, 1.0); task.putvartype(voff_y + j, mosek.variabletype.type_int); } // Linear constraints // - Total budget task.appendcons(1); task.putconname(coff_bud, "budget"); for (int j = 0; j < n; ++j) { /* Coefficients in the first row of A */ task.putaij(coff_bud, voff_x + j, 1.0); task.putaij(coff_bud, voff_z + j, g[j]); task.putaij(coff_bud, voff_y + j, f[j]); } double U = w; for (int i = 0; i < n; ++i) { U += x0[i]; } task.putconbound(coff_bud, mosek.boundkey.fx, U, U); // - Absolute value task.appendcons(2 * n); for (int i = 0; i < n; ++i) { task.putconname(coff_abs1 + i, "zabs1[" + (1 + i) + "]"); task.putaij(coff_abs1 + i, voff_x + i, -1.0); task.putaij(coff_abs1 + i, voff_z + i, 1.0); task.putconbound(coff_abs1 + i, mosek.boundkey.lo, -x0[i], infinity); task.putconname(coff_abs2 + i, "zabs2[" + (1 + i) + "]"); task.putaij(coff_abs2 + i, voff_x + i, 1.0); task.putaij(coff_abs2 + i, voff_z + i, 1.0); task.putconbound(coff_abs2 + i, mosek.boundkey.lo, x0[i], infinity); } // - Switch task.appendcons(n); for (int i = 0; i < n; ++i) { task.putconname(coff_swi + i, "switch[" + (1 + i) + "]"); task.putaij(coff_swi + i, voff_z + i, 1.0); task.putaij(coff_swi + i, voff_y + i, -U); task.putconbound(coff_swi + i, mosek.boundkey.up, -infinity, 0.0); } // ACCs int aoff_q = 0; // - (gamma, GTx) in Q(k+1) // The part of F and g for variable x: // [0, 0, 0] [gamma] // F = [GT, 0, 0], g = [0 ] task.appendafes(k + 1); task.putafeg(aoff_q, gamma); int[] vslice_x = new int[n]; double[] GT_row = new double[n]; for (int i = 0; i < n; ++i) { vslice_x[i] = voff_x + i; } for (int i = 0; i < k; ++i) { for (int j = 0; j < n; ++j) GT_row[j] = GT[i, j]; task.putafefrow(aoff_q + i + 1, vslice_x, GT_row); } long qdom = task.appendquadraticconedomain(k + 1); task.appendaccseq(qdom, aoff_q, null); task.putaccname(aoff_q, "risk"); // Objective: maximize expected return mu^T x for (int j = 0; j < n; ++j) { task.putcj(voff_x + j, mu[j]); } task.putobjsense(mosek.objsense.maximize); //Turn all log output off. //task.putintparam(mosek.iparam.log,0); task.writedata("dump.ptf"); /* Solve the problem */ task.optimize(); task.solutionsummary(mosek.streamtype.log); // Check if the interior point solution is an optimal point solsta solsta = task.getsolsta(mosek.soltype.itg); if (solsta != mosek.solsta.integer_optimal) { // See https://docs.mosek.com/latest/dotnetapi/accessing-solution.html about handling solution statuses. throw new Exception(rescode.err_unhandled_solution_status, String.Format("Unexpected solution status: {0}", solsta)); } double expret = 0.0; double[] xx = task.getxx(mosek.soltype.itg); for (int j = 0; j < n; ++j) expret += mu[j] * xx[j + voff_x]; Console.WriteLine("Expected return {0:E6} for gamma {1:E6}\n\n", expret, gamma); } } } }