examples/notebook/pdlp/simple_pdlp_program.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Solves a simple LP using PDLP's direct Python API.
Note: The direct API is generally for advanced use cases. It is matrix-based, that is, you specify the LP using matrices and vectors instead of algebraic expressions. You can also use PDLP via the algebraic pywraplp API (see linear_solver/samples/simple_lp_program.py).
import numpy as np
import scipy.sparse
from ortools.pdlp import solve_log_pb2
from ortools.pdlp import solvers_pb2
from ortools.pdlp.python import pdlp
from ortools.init.python import init
def simple_lp() -> pdlp.QuadraticProgram:
"""Returns a small LP.
min 5.5 x_0 - 2 x_1 - x_2 + x_3 - 14 s.t.
2 x_0 + x_1 + x_2 + 2 x_3 = 12
x_0 + x_2 <= 7
4 x_0 >= -4
-1 <= 1.5 x_2 - x_3 <= 1
-infinity <= x_0 <= infinity
-2 <= x_1 <= infinity
-infinity <= x_2 <= 6
2.5 <= x_3 <= 3.5
"""
lp = pdlp.QuadraticProgram()
lp.objective_offset = -14
lp.objective_vector = [5.5, -2, -1, 1]
lp.constraint_lower_bounds = [12, -np.inf, -4, -1]
lp.constraint_upper_bounds = [12, 7, np.inf, 1]
lp.variable_lower_bounds = [-np.inf, -2, -np.inf, 2.5]
lp.variable_upper_bounds = [np.inf, np.inf, 6, 3.5]
# Most use cases should initialize the sparse constraint matrix without
# constructing a dense matrix first! We use a np.array here for convenience
# only.
constraint_matrix = np.array(
[[2, 1, 1, 2], [1, 0, 1, 0], [4, 0, 0, 0], [0, 0, 1.5, -1]]
)
lp.constraint_matrix = scipy.sparse.csc_matrix(constraint_matrix)
return lp
def main() -> None:
params = solvers_pb2.PrimalDualHybridGradientParams()
# Below are some common parameters to modify. Here, we just re-assign the
# defaults.
optimality_criteria = params.termination_criteria.simple_optimality_criteria
optimality_criteria.eps_optimal_relative = 1.0e-6
optimality_criteria.eps_optimal_absolute = 1.0e-6
params.termination_criteria.time_sec_limit = np.inf
params.num_threads = 1
params.verbosity_level = 0
params.presolve_options.use_glop = False
# Call the main solve function.
result = pdlp.primal_dual_hybrid_gradient(simple_lp(), params)
solve_log = result.solve_log
if solve_log.termination_reason == solve_log_pb2.TERMINATION_REASON_OPTIMAL:
print("Solve successful")
else:
print(
"Solve not successful. Status:",
solve_log_pb2.TerminationReason.Name(solve_log.termination_reason),
)
# Solutions vectors are always returned. *However*, their interpretation
# depends on termination_reason! See primal_dual_hybrid_gradient.h for more
# details on what the vectors mean if termination_reason is not
# TERMINATION_REASON_OPTIMAL.
print("Primal solution:", result.primal_solution)
print("Dual solution:", result.dual_solution)
print("Reduced costs:", result.reduced_costs)
solution_type = solve_log.solution_type
print("Solution type:", solve_log_pb2.PointType.Name(solution_type))
for ci in solve_log.solution_stats.convergence_information:
if ci.candidate_type == solution_type:
print("Primal objective:", ci.primal_objective)
print("Dual objective:", ci.dual_objective)
print("Iterations:", solve_log.iteration_count)
print("Solve time (sec):", solve_log.solve_time_sec)
init.CppBridge.init_logging("simple_pdlp_program.py")
cpp_flags = init.CppFlags()
cpp_flags.stderrthreshold = 0
cpp_flags.log_prefix = False
init.CppBridge.set_flags(cpp_flags)
main()