Exploit dual degeneracy to reduce the number of integer infeasibilities; add primal simplex

cpp/include/cuopt/mathematical_optimization/constants.h

@@ -53,6 +53,7 @@
 #define CUOPT_ELIMINATE_DENSE_COLUMNS              "eliminate_dense_columns"
 #define CUOPT_CUDSS_DETERMINISTIC                  "cudss_deterministic"
 #define CUOPT_PRESOLVE                             "presolve"
+#define CUOPT_INITIAL_PERTURBATION                 "initial_perturbation"
 #define CUOPT_MIP_PROBING                          "mip_probing"
 #define CUOPT_DUAL_POSTSOLVE                       "dual_postsolve"
 #define CUOPT_MIP_DETERMINISM_MODE                 "mip_determinism_mode"
@@ -198,7 +199,8 @@
 #define CUOPT_METHOD_PDLP         1
 #define CUOPT_METHOD_DUAL_SIMPLEX 2
 #define CUOPT_METHOD_BARRIER      3
-#define CUOPT_METHOD_UNSET        4
+#define CUOPT_METHOD_PRIMAL       4
+#define CUOPT_METHOD_UNSET        5
 
 /* @brief PDLP precision mode constants */
 #define CUOPT_PDLP_DEFAULT_PRECISION -1

cpp/include/cuopt/mathematical_optimization/pdlp/solver_settings.hpp

@@ -59,6 +59,7 @@ enum pdlp_solver_mode_t : int {
  * PDLP: Use the PDLP method.
  * DualSimplex: Use the dual simplex method.
  * Barrier: Use the barrier method
+ * Primal: Use the (experimental) primal simplex method.
  * Unset: The value was not set.
  *
  * @note Default method is Concurrent.
@@ -68,6 +69,7 @@ enum method_t : int {
   PDLP        = CUOPT_METHOD_PDLP,
   DualSimplex = CUOPT_METHOD_DUAL_SIMPLEX,
   Barrier     = CUOPT_METHOD_BARRIER,
+  Primal      = CUOPT_METHOD_PRIMAL,
   Unset       = CUOPT_METHOD_UNSET
 };
 
@@ -79,6 +81,7 @@ inline std::string method_to_string(method_t method)
     case method_t::PDLP: return "PDLP";
     case method_t::Barrier: return "Barrier";
     case method_t::Concurrent: return "Concurrent";
+    case method_t::Primal: return "Primal Simplex";
     default: return "Unset";
   }
 }
@@ -294,6 +297,7 @@ class pdlp_solver_settings_t {
   i_t augmented{-1};
   i_t dualize{-1};
   i_t ordering{-1};
+  i_t initial_perturbation{-1};
   i_t barrier_dual_initial_point{-1};
   i_t postsolve_info{-1};
   // Ruiz equilibration for QCQP (barrier) scaling: -1 automatic (row/column