192 lines
6.7 KiB
Plaintext
192 lines
6.7 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "google",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Copyright 2025 Google LLC."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "apache",
|
|
"metadata": {},
|
|
"source": [
|
|
"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
|
|
"you may not use this file except in compliance with the License.\n",
|
|
"You may obtain a copy of the License at\n",
|
|
"\n",
|
|
" http://www.apache.org/licenses/LICENSE-2.0\n",
|
|
"\n",
|
|
"Unless required by applicable law or agreed to in writing, software\n",
|
|
"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
|
|
"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
|
|
"See the License for the specific language governing permissions and\n",
|
|
"limitations under the License.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "basename",
|
|
"metadata": {},
|
|
"source": [
|
|
"# simple_pdlp_program"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "link",
|
|
"metadata": {},
|
|
"source": [
|
|
"<table align=\"left\">\n",
|
|
"<td>\n",
|
|
"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/pdlp/simple_pdlp_program.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
|
|
"</td>\n",
|
|
"<td>\n",
|
|
"<a href=\"https://github.com/google/or-tools/blob/main/ortools/pdlp/samples/simple_pdlp_program.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
|
|
"</td>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "doc",
|
|
"metadata": {},
|
|
"source": [
|
|
"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "install",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"%pip install ortools"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "description",
|
|
"metadata": {},
|
|
"source": [
|
|
"\n",
|
|
"Solves a simple LP using PDLP's direct Python API.\n",
|
|
"\n",
|
|
"Note: The direct API is generally for advanced use cases. It is matrix-based,\n",
|
|
"that is, you specify the LP using matrices and vectors instead of algebraic\n",
|
|
"expressions. You can also use PDLP via the algebraic pywraplp API (see\n",
|
|
"linear_solver/samples/simple_lp_program.py).\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "code",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import scipy.sparse\n",
|
|
"\n",
|
|
"from ortools.pdlp import solve_log_pb2\n",
|
|
"from ortools.pdlp import solvers_pb2\n",
|
|
"from ortools.pdlp.python import pdlp\n",
|
|
"from ortools.init.python import init\n",
|
|
"\n",
|
|
"\n",
|
|
"def simple_lp() -> pdlp.QuadraticProgram:\n",
|
|
" \"\"\"Returns a small LP.\n",
|
|
"\n",
|
|
" min 5.5 x_0 - 2 x_1 - x_2 + x_3 - 14 s.t.\n",
|
|
" 2 x_0 + x_1 + x_2 + 2 x_3 = 12\n",
|
|
" x_0 + x_2 <= 7\n",
|
|
" 4 x_0 >= -4\n",
|
|
" -1 <= 1.5 x_2 - x_3 <= 1\n",
|
|
" -infinity <= x_0 <= infinity\n",
|
|
" -2 <= x_1 <= infinity\n",
|
|
" -infinity <= x_2 <= 6\n",
|
|
" 2.5 <= x_3 <= 3.5\n",
|
|
" \"\"\"\n",
|
|
" lp = pdlp.QuadraticProgram()\n",
|
|
" lp.objective_offset = -14\n",
|
|
" lp.objective_vector = [5.5, -2, -1, 1]\n",
|
|
" lp.constraint_lower_bounds = [12, -np.inf, -4, -1]\n",
|
|
" lp.constraint_upper_bounds = [12, 7, np.inf, 1]\n",
|
|
" lp.variable_lower_bounds = [-np.inf, -2, -np.inf, 2.5]\n",
|
|
" lp.variable_upper_bounds = [np.inf, np.inf, 6, 3.5]\n",
|
|
" # Most use cases should initialize the sparse constraint matrix without\n",
|
|
" # constructing a dense matrix first! We use a np.array here for convenience\n",
|
|
" # only.\n",
|
|
" constraint_matrix = np.array(\n",
|
|
" [[2, 1, 1, 2], [1, 0, 1, 0], [4, 0, 0, 0], [0, 0, 1.5, -1]]\n",
|
|
" )\n",
|
|
" lp.constraint_matrix = scipy.sparse.csc_matrix(constraint_matrix)\n",
|
|
" return lp\n",
|
|
"\n",
|
|
"\n",
|
|
"def main() -> None:\n",
|
|
" params = solvers_pb2.PrimalDualHybridGradientParams()\n",
|
|
" # Below are some common parameters to modify. Here, we just re-assign the\n",
|
|
" # defaults.\n",
|
|
" optimality_criteria = params.termination_criteria.simple_optimality_criteria\n",
|
|
" optimality_criteria.eps_optimal_relative = 1.0e-6\n",
|
|
" optimality_criteria.eps_optimal_absolute = 1.0e-6\n",
|
|
" params.termination_criteria.time_sec_limit = np.inf\n",
|
|
" params.num_threads = 1\n",
|
|
" params.verbosity_level = 0\n",
|
|
" params.presolve_options.use_glop = False\n",
|
|
"\n",
|
|
" # Call the main solve function.\n",
|
|
" result = pdlp.primal_dual_hybrid_gradient(simple_lp(), params)\n",
|
|
" solve_log = result.solve_log\n",
|
|
"\n",
|
|
" if solve_log.termination_reason == solve_log_pb2.TERMINATION_REASON_OPTIMAL:\n",
|
|
" print(\"Solve successful\")\n",
|
|
" else:\n",
|
|
" print(\n",
|
|
" \"Solve not successful. Status:\",\n",
|
|
" solve_log_pb2.TerminationReason.Name(solve_log.termination_reason),\n",
|
|
" )\n",
|
|
"\n",
|
|
" # Solutions vectors are always returned. *However*, their interpretation\n",
|
|
" # depends on termination_reason! See primal_dual_hybrid_gradient.h for more\n",
|
|
" # details on what the vectors mean if termination_reason is not\n",
|
|
" # TERMINATION_REASON_OPTIMAL.\n",
|
|
" print(\"Primal solution:\", result.primal_solution)\n",
|
|
" print(\"Dual solution:\", result.dual_solution)\n",
|
|
" print(\"Reduced costs:\", result.reduced_costs)\n",
|
|
"\n",
|
|
" solution_type = solve_log.solution_type\n",
|
|
" print(\"Solution type:\", solve_log_pb2.PointType.Name(solution_type))\n",
|
|
" for ci in solve_log.solution_stats.convergence_information:\n",
|
|
" if ci.candidate_type == solution_type:\n",
|
|
" print(\"Primal objective:\", ci.primal_objective)\n",
|
|
" print(\"Dual objective:\", ci.dual_objective)\n",
|
|
"\n",
|
|
" print(\"Iterations:\", solve_log.iteration_count)\n",
|
|
" print(\"Solve time (sec):\", solve_log.solve_time_sec)\n",
|
|
"\n",
|
|
"\n",
|
|
"init.CppBridge.init_logging(\"simple_pdlp_program.py\")\n",
|
|
"cpp_flags = init.CppFlags()\n",
|
|
"cpp_flags.stderrthreshold = 0\n",
|
|
"cpp_flags.log_prefix = False\n",
|
|
"init.CppBridge.set_flags(cpp_flags)\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"name": "python"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|