implement vaidya minimizer and hessian computation

Author: TolisChal

include/preprocess/inscribed_ellipsoid_rounding.hpp

@@ -26,7 +26,8 @@ compute_inscribed_ellipsoid(Custom_MT A, VT b, VT const& x0,
     {
         return max_inscribed_ellipsoid<MT>(A, b, x0, maxiter, tol, reg);
     } else if constexpr (ellipsoid_type == EllipsoidType::LOG_BARRIER ||
-                         ellipsoid_type == EllipsoidType::VOLUMETRIC_BARRIER)
+                         ellipsoid_type == EllipsoidType::VOLUMETRIC_BARRIER ||
+                         ellipsoid_type == EllipsoidType::VAIDYA_BARRIER)
     {
         return barrier_center_ellipsoid_linear_ineq<MT, ellipsoid_type, NT>(A, b, x0);
     } else

include/preprocess/rounding_util_functions.hpp

@@ -22,7 +22,8 @@ enum EllipsoidType
 {
   MAX_ELLIPSOID = 1,
   LOG_BARRIER = 2,
-  VOLUMETRIC_BARRIER = 3
+  VOLUMETRIC_BARRIER = 3,
+  VAIDYA_BARRIER = 4
 };
 
 template <int T>
@@ -345,7 +346,8 @@ std::tuple<NT, NT> init_step()
   if constexpr (BarrierType == EllipsoidType::LOG_BARRIER)
   {
     return {NT(1), NT(0.99)};
-  } else if constexpr (BarrierType == EllipsoidType::VOLUMETRIC_BARRIER)
+  } else if constexpr (BarrierType == EllipsoidType::VOLUMETRIC_BARRIER ||
+                       BarrierType == EllipsoidType::VAIDYA_BARRIER)
   {
     return {NT(0.5), NT(0.4)};
   } else {
@@ -362,21 +364,43 @@ void get_barrier_hessian_grad(MT const& A, MT const& A_trans, VT const& b,
   b_Ax.noalias() = b - Ax;
   VT s = b_Ax.cwiseInverse();
   VT s_sq = s.cwiseProduct(s);
+  VT sigma;
   // Hessian of the log-barrier function
   update_Atrans_Diag_A<NT>(H, A_trans, A, s_sq.asDiagonal());
+
+  if constexpr (BarrierType == EllipsoidType::VOLUMETRIC_BARRIER ||
+                BarrierType == EllipsoidType::VAIDYA_BARRIER)
+  {
+    // Computing sigma(x)_i = (a_i^T H^{-1} a_i) / (b_i - a_i^Tx)^2
+    MT_dense HA = solve_mat(llt, H, A_trans, obj_val);
+    MT_dense aiHai = HA.transpose().cwiseProduct(A);
+    sigma = (aiHai.rowwise().sum()).cwiseProduct(s_sq);
+  }
+
   if constexpr (BarrierType == EllipsoidType::LOG_BARRIER)
   {
     grad.noalias() = A_trans * s;
   } else if constexpr (BarrierType == EllipsoidType::VOLUMETRIC_BARRIER)
   {
-    // Computing sigma(x)_i = (a_i^T H^{-1} a_i) / (b_i - a_i^Tx)^2
-    MT_dense HA = solve_mat(llt, H, A_trans, obj_val);
-    MT_dense aiHai = HA.transpose().cwiseProduct(A);
-    VT sigma = (aiHai.rowwise().sum()).cwiseProduct(s_sq);
     // Gradient of the volumetric barrier function
     grad.noalias() = A_trans * (s.cwiseProduct(sigma));
     // Hessian of the volumetric barrier function
     update_Atrans_Diag_A<NT>(H, A_trans, A, s_sq.cwiseProduct(sigma).asDiagonal());
+  } else if constexpr (BarrierType == EllipsoidType::VAIDYA_BARRIER)
+  {
+    const int m = b.size(), d = x.size();
+    // Weighted gradient of the log barrier function
+    grad.noalias() = A_trans * s;
+    grad *= NT(d) / NT(m);
+    // Add the gradient of the volumetric function
+    grad.noalias() += A_trans * (s.cwiseProduct(sigma));
+    // Weighted Hessian of the log barrier function
+    H *= NT(d) / NT(m);
+    // Add the Hessian of the volumetric function
+    MT Hvol(d, d);
+    update_Atrans_Diag_A<NT>(Hvol, A_trans, A, s_sq.cwiseProduct(sigma).asDiagonal());
+    H += Hvol;
+    obj_val -= s.array().log().sum();
   } else {
     static_assert(AssertBarrierFalseType<BarrierType>::value,
             "Barrier type is not supported.");
@@ -393,6 +417,9 @@ void get_step_next_iteration(NT const obj_val_prev, NT const obj_val,
   } else if constexpr (BarrierType == EllipsoidType::VOLUMETRIC_BARRIER)
   {
     step_iter *= (obj_val_prev <= obj_val - tol_obj) ? NT(0.9) : NT(0.999);
+  } else if constexpr (BarrierType == EllipsoidType::VAIDYA_BARRIER)
+  {
+    step_iter *= NT(0.999);
   } else {
     static_assert(AssertBarrierFalseType<BarrierType>::value,
             "Barrier type is not supported.");