112 lines
4.2 KiB
Python
112 lines
4.2 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2025 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Solves a simple LP using PDLP's direct Python API.
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Note: The direct API is generally for advanced use cases. It is matrix-based,
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that is, you specify the LP using matrices and vectors instead of algebraic
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expressions. You can also use PDLP via the algebraic pywraplp API (see
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linear_solver/samples/simple_lp_program.py).
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"""
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import numpy as np
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import scipy.sparse
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from ortools.pdlp import solve_log_pb2
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from ortools.pdlp import solvers_pb2
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from ortools.pdlp.python import pdlp
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from ortools.init.python import init
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def simple_lp() -> pdlp.QuadraticProgram:
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"""Returns a small LP.
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min 5.5 x_0 - 2 x_1 - x_2 + x_3 - 14 s.t.
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2 x_0 + x_1 + x_2 + 2 x_3 = 12
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x_0 + x_2 <= 7
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4 x_0 >= -4
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-1 <= 1.5 x_2 - x_3 <= 1
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-infinity <= x_0 <= infinity
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-2 <= x_1 <= infinity
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-infinity <= x_2 <= 6
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2.5 <= x_3 <= 3.5
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"""
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lp = pdlp.QuadraticProgram()
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lp.objective_offset = -14
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lp.objective_vector = [5.5, -2, -1, 1]
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lp.constraint_lower_bounds = [12, -np.inf, -4, -1]
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lp.constraint_upper_bounds = [12, 7, np.inf, 1]
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lp.variable_lower_bounds = [-np.inf, -2, -np.inf, 2.5]
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lp.variable_upper_bounds = [np.inf, np.inf, 6, 3.5]
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# Most use cases should initialize the sparse constraint matrix without
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# constructing a dense matrix first! We use a np.array here for convenience
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# only.
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constraint_matrix = np.array(
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[[2, 1, 1, 2], [1, 0, 1, 0], [4, 0, 0, 0], [0, 0, 1.5, -1]]
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)
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lp.constraint_matrix = scipy.sparse.csc_matrix(constraint_matrix)
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return lp
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def main() -> None:
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params = solvers_pb2.PrimalDualHybridGradientParams()
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# Below are some common parameters to modify. Here, we just re-assign the
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# defaults.
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optimality_criteria = params.termination_criteria.simple_optimality_criteria
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optimality_criteria.eps_optimal_relative = 1.0e-6
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optimality_criteria.eps_optimal_absolute = 1.0e-6
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params.termination_criteria.time_sec_limit = np.inf
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params.num_threads = 1
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params.verbosity_level = 0
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params.presolve_options.use_glop = False
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# Call the main solve function.
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result = pdlp.primal_dual_hybrid_gradient(simple_lp(), params)
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solve_log = result.solve_log
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if solve_log.termination_reason == solve_log_pb2.TERMINATION_REASON_OPTIMAL:
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print("Solve successful")
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else:
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print(
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"Solve not successful. Status:",
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solve_log_pb2.TerminationReason.Name(solve_log.termination_reason),
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)
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# Solutions vectors are always returned. *However*, their interpretation
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# depends on termination_reason! See primal_dual_hybrid_gradient.h for more
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# details on what the vectors mean if termination_reason is not
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# TERMINATION_REASON_OPTIMAL.
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print("Primal solution:", result.primal_solution)
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print("Dual solution:", result.dual_solution)
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print("Reduced costs:", result.reduced_costs)
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solution_type = solve_log.solution_type
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print("Solution type:", solve_log_pb2.PointType.Name(solution_type))
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for ci in solve_log.solution_stats.convergence_information:
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if ci.candidate_type == solution_type:
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print("Primal objective:", ci.primal_objective)
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print("Dual objective:", ci.dual_objective)
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print("Iterations:", solve_log.iteration_count)
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print("Solve time (sec):", solve_log.solve_time_sec)
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if __name__ == "__main__":
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init.CppBridge.init_logging("simple_pdlp_program.py")
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cpp_flags = init.CppFlags()
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cpp_flags.stderrthreshold = 0
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cpp_flags.log_prefix = False
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init.CppBridge.set_flags(cpp_flags)
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main()
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