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primal_dual_hybrid_gradient_test.cc
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// Copyright 2010-2022 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "ortools/pdlp/primal_dual_hybrid_gradient.h"
#include <algorithm>
#include <atomic>
#include <cmath>
#include <cstdint>
#include <limits>
#include <optional>
#include <ostream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
#include "Eigen/Core"
#include "Eigen/SparseCore"
#include "absl/container/flat_hash_map.h"
#include "absl/log/check.h"
#include "absl/status/status.h"
#include "absl/status/statusor.h"
#include "absl/strings/str_cat.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
#include "ortools/base/logging.h"
#include "ortools/glop/parameters.pb.h"
#include "ortools/linear_solver/linear_solver.pb.h"
#include "ortools/lp_data/lp_data.h"
#include "ortools/lp_data/lp_types.h"
#include "ortools/pdlp/iteration_stats.h"
#include "ortools/pdlp/quadratic_program.h"
#include "ortools/pdlp/quadratic_program_io.h"
#include "ortools/pdlp/sharded_quadratic_program.h"
#include "ortools/pdlp/solve_log.pb.h"
#include "ortools/pdlp/solvers.pb.h"
#include "ortools/pdlp/termination.h"
#include "ortools/pdlp/test_util.h"
namespace operations_research::pdlp {
namespace {
using ::Eigen::VectorXd;
using ::operations_research::glop::ConstraintStatus;
using ::operations_research::glop::VariableStatus;
using ::testing::_;
using ::testing::AnyNumber;
using ::testing::AnyOf;
using ::testing::DoubleNear;
using ::testing::ElementsAre;
using ::testing::Eq;
using ::testing::Ge;
using ::testing::HasSubstr;
using ::testing::IsEmpty;
using ::testing::Not;
using ::testing::Pair;
using ::testing::SizeIs;
using ::testing::UnorderedElementsAre;
const double kInfinity = std::numeric_limits<double>::infinity();
} // namespace
// ITERATION_TYPE_CONSIDER_CASE(x) expands to print the iteration type x to *os.
// Using this macro prevents typos in the strings.
#define ITERATION_TYPE_CONSIDER_CASE(x) \
case IterationType::x: \
*os << #x; \
break
// NOTE: `PrintTo(IterationType, std::ostream*)` needs to be in the same
// namespace as `IterationType`.
void PrintTo(IterationType iteration_type, std::ostream* os) {
switch (iteration_type) {
ITERATION_TYPE_CONSIDER_CASE(kNormal);
ITERATION_TYPE_CONSIDER_CASE(kPrimalFeasibility);
ITERATION_TYPE_CONSIDER_CASE(kDualFeasibility);
ITERATION_TYPE_CONSIDER_CASE(kNormalTermination);
ITERATION_TYPE_CONSIDER_CASE(kPresolveTermination);
ITERATION_TYPE_CONSIDER_CASE(kFeasibilityPolishingTermination);
}
}
#undef ITERATION_TYPE_CONSIDER_CASE
namespace {
PrimalDualHybridGradientParams CreateSolverParams(
const int iteration_limit, const double eps_optimal_absolute,
const bool enable_scaling, const int num_threads,
const bool use_iteration_limit, const bool use_malitsky_pock_linesearch,
const bool use_diagonal_qp_trust_region_solver) {
PrimalDualHybridGradientParams params;
if (!enable_scaling) {
params.set_l2_norm_rescaling(false);
params.set_l_inf_ruiz_iterations(0);
}
if (use_malitsky_pock_linesearch) {
params.set_linesearch_rule(
PrimalDualHybridGradientParams::MALITSKY_POCK_LINESEARCH_RULE);
}
params.mutable_termination_criteria()
->mutable_simple_optimality_criteria()
->set_eps_optimal_relative(0.0);
if (use_iteration_limit) {
// This effectively forces convergence on the iteration limit only.
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.mutable_termination_criteria()
->mutable_simple_optimality_criteria()
->set_eps_optimal_absolute(0.0);
} else {
params.mutable_termination_criteria()
->mutable_simple_optimality_criteria()
->set_eps_optimal_absolute(eps_optimal_absolute);
}
if (use_diagonal_qp_trust_region_solver) {
params.set_use_diagonal_qp_trust_region_solver(true);
params.set_diagonal_qp_trust_region_solver_tolerance(1.0e-8);
}
params.set_num_threads(num_threads);
return params;
}
// Verifies expected termination reason and iteration count for an instance
// where an optimal solution exists.
// `params` must have been generated by `CreateSolverParams()` with the same
// `use_iteration_limit`.
// Intended usage:
// const bool use_iteration_limit = ...;
// PrimalDualHybridGradientParams params =
// CreateSolverParams(..., use_iteration_limit, ...);
// SolverResult output = PrimalDualHybridGradient(..., params);
// VerifyTerminationReasonAndIterationCount(params, output,
// use_iteration_limit);
void VerifyTerminationReasonAndIterationCount(
const PrimalDualHybridGradientParams& params, const SolverResult& output,
const bool use_iteration_limit) {
if (use_iteration_limit) {
// When a PDHG step has zero length PDHG can no longer make progress and
// hence terminates immediately. In theory a zero step length implies
// optimality but in practice PDHG terminates with a reason of OPTIMAL if
// the optimality checks pass and NUMERICAL_ERROR otherwise.
// When `use_iteration_limit==true`, `CreateSolverParams()` sets all the
// epsilons to 0, which makes the optimality checks harder to pass but not
// impossible. Both OPTIMAL and NUMERICAL_ERROR are therefore ok termination
// reasons.
EXPECT_THAT(
output.solve_log.termination_reason(),
AnyOf(TERMINATION_REASON_ITERATION_LIMIT,
TERMINATION_REASON_NUMERICAL_ERROR, TERMINATION_REASON_OPTIMAL));
if (output.solve_log.termination_reason() ==
TERMINATION_REASON_ITERATION_LIMIT) {
EXPECT_EQ(output.solve_log.iteration_count(),
params.termination_criteria().iteration_limit());
} else {
EXPECT_LE(output.solve_log.iteration_count(),
params.termination_criteria().iteration_limit());
}
} else {
EXPECT_EQ(output.solve_log.termination_reason(),
TERMINATION_REASON_OPTIMAL);
EXPECT_LE(output.solve_log.iteration_count(),
params.termination_criteria().iteration_limit());
}
}
// Verifies the primal and dual objective values.
void VerifyObjectiveValues(const SolverResult& result,
const double objective_value,
const double tolerance) {
const auto& convergence_info = GetConvergenceInformation(
result.solve_log.solution_stats(), result.solve_log.solution_type());
ASSERT_TRUE(convergence_info.has_value());
EXPECT_THAT(convergence_info->primal_objective(),
DoubleNear(objective_value, tolerance));
EXPECT_THAT(convergence_info->dual_objective(),
DoubleNear(objective_value, tolerance));
}
class PrimalDualHybridGradientLPTest
: public testing::TestWithParam<
std::tuple</*enable_scaling=*/bool, /*num_threads=*/int,
/*use_iteration_limit=*/bool,
/*use_malitsky_pock_linesearch=*/bool>> {
protected:
PrimalDualHybridGradientParams CreateSolverParamsForFixture(
const int iteration_limit, const double eps_optimal_absolute) {
const auto [enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch] = GetParam();
return CreateSolverParams(iteration_limit, eps_optimal_absolute,
enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch,
/*use_diagonal_qp_trust_region_solver=*/false);
}
void VerifyTerminationReasonAndIterationCountForFixture(
const PrimalDualHybridGradientParams& params,
const SolverResult& output) {
const auto [enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch] = GetParam();
VerifyTerminationReasonAndIterationCount(params, output,
use_iteration_limit);
}
};
class PrimalDualHybridGradientDiagonalQPTest
: public testing::TestWithParam<
std::tuple</*enable_scaling=*/bool, /*num_threads=*/int,
/*use_iteration_limit=*/bool,
/*use_malitsky_pock_linesearch=*/bool,
/*use_diagonal_qp_trust_region_solver=*/bool>> {
protected:
PrimalDualHybridGradientParams CreateSolverParamsForFixture(
const int iteration_limit, const double eps_optimal_absolute) {
const auto [enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch,
use_diagonal_qp_trust_region_solver] = GetParam();
return CreateSolverParams(iteration_limit, eps_optimal_absolute,
enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch,
use_diagonal_qp_trust_region_solver);
}
void VerifyTerminationReasonAndIterationCountForFixture(
const PrimalDualHybridGradientParams& params,
const SolverResult& output) {
const auto [enable_scaling, num_threads, use_iteration_limit,
use_malitsky_pock_linesearch,
use_diagonal_qp_trust_region_solver] = GetParam();
VerifyTerminationReasonAndIterationCount(params, output,
use_iteration_limit);
}
};
class PrimalDualHybridGradientVerbosityTest
: public testing::TestWithParam</*verbosity_level=*/int> {};
class PresolveDualScalingTest
: public testing::TestWithParam<
std::tuple</*Dualize=*/bool,
/*NegateAndScaleObjective=*/bool>> {};
INSTANTIATE_TEST_SUITE_P(
QP, PrimalDualHybridGradientDiagonalQPTest,
testing::Combine(testing::Bool(), testing::Values(1, 4), testing::Bool(),
testing::Bool(), testing::Bool()),
[](const testing::TestParamInfo<
PrimalDualHybridGradientDiagonalQPTest::ParamType>& info) {
return absl::StrCat(
std::get<0>(info.param) ? "Scaling" : "NoScaling", "_",
std::get<1>(info.param), "Threads_",
std::get<2>(info.param) ? "IterationLimit" : "NoIterationLimit", "_",
std::get<3>(info.param) ? "MalitskyPockLinesearch"
: "AdaptiveLinesearch",
"_", std::get<4>(info.param) ? "TRSolverDiag" : "TRSolverNoDiag");
});
INSTANTIATE_TEST_SUITE_P(
LP, PrimalDualHybridGradientLPTest,
testing::Combine(testing::Bool(), testing::Values(1, 4), testing::Bool(),
testing::Bool()),
[](const testing::TestParamInfo<PrimalDualHybridGradientLPTest::ParamType>&
info) {
return absl::StrCat(
std::get<0>(info.param) ? "Scaling" : "NoScaling", "_",
std::get<1>(info.param), "Threads_",
std::get<2>(info.param) ? "IterationLimit" : "NoIterationLimit", "_",
std::get<3>(info.param) ? "MalitskyPockLinesearch"
: "AdaptiveLinesearch");
});
INSTANTIATE_TEST_SUITE_P(Verbosity, PrimalDualHybridGradientVerbosityTest,
testing::Values(0, 1, 2, 3, 4));
INSTANTIATE_TEST_SUITE_P(
PresolveDualScaling, PresolveDualScalingTest,
testing::Combine(testing::Bool(), testing::Bool()),
[](const testing::TestParamInfo<PresolveDualScalingTest::ParamType>& info) {
return absl::StrCat(std::get<1>(info.param) ? "Dualize" : "NoDualize",
std::get<0>(info.param) ? "NegateAndScaleObjective"
: "NoObjectiveScaling");
});
TEST_P(PrimalDualHybridGradientLPTest, UnboundedVariables) {
const int iteration_upperbound = 980;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-7);
params.set_major_iteration_frequency(100);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, -34.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({-1, 8, 1, 2.5}, 1.0e-4));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({-2, 0, 2.375, 2.0 / 3}, 1.0e-4));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 4);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 4);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 4);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 4);
}
TEST_P(PrimalDualHybridGradientLPTest, Tiny) {
const int iteration_upperbound = 300;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-5);
params.set_major_iteration_frequency(60);
SolverResult output = PrimalDualHybridGradient(TinyLp(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, -1.0, 1.0e-4);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({1, 0, 6, 2}, 1.0e-4));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({0.5, 4.0, 0.0}, 1.0e-4));
EXPECT_THAT(output.reduced_costs,
EigenArrayNear<double>({0.0, 1.5, -3.5, 0.0}, 1.0e-4));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 4);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 4);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 3);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 3);
}
TEST_P(PrimalDualHybridGradientLPTest, CorrelationClusteringOne) {
const int iteration_upperbound = 9;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-10);
params.set_major_iteration_frequency(2);
SolverResult output =
PrimalDualHybridGradient(CorrelationClusteringLp(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 1.0, 1.0e-14);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({1, 1, 0, 1, 0, 0}, 1.0e-14));
ASSERT_EQ(output.dual_solution.size(), 3);
// There are multiple optimal dual solutions.
EXPECT_GE(output.dual_solution[0], 0);
EXPECT_GE(output.dual_solution[1], 0);
EXPECT_GE(output.dual_solution[2], 0);
EXPECT_GE(output.dual_solution[0] + output.dual_solution[1], 1 - 1.0e-14);
const auto& convergence_information = GetConvergenceInformation(
output.solve_log.solution_stats(), output.solve_log.solution_type());
ASSERT_TRUE(convergence_information.has_value());
EXPECT_THAT(convergence_information->corrected_dual_objective(),
DoubleNear(1, 1.0e-14));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 6);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 6);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 3);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 3);
}
TEST_P(PrimalDualHybridGradientLPTest, CorrelationClusteringStar) {
const int iteration_upperbound = 45;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(5);
SolverResult output =
PrimalDualHybridGradient(CorrelationClusteringStarLp(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 1.5, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({0.5, 0.5, 0.5, 0.0, 0.0, 0.0}, 1.0e-6));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({0.5, 0.5, 0.5}, 1.0e-6));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 6);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 6);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 3);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 3);
}
// A double-sided constraint l <= a^T x <= u where neither constraint is tight
// at optimum could cause the trust region solver to malfunction if we picked
// the wrong dual subgradient. This test verifies that we solve an instance with
// such a constraint quickly to high accuracy.
TEST_P(PrimalDualHybridGradientLPTest, InactiveTwoSidedConstraint) {
const int iteration_upperbound = 500;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-8);
params.set_major_iteration_frequency(60);
QuadraticProgram qp = TestLp();
// This makes this constraint double-sided and inactive at the optimal
// solution.
qp.constraint_lower_bounds[1] = -10;
SolverResult output = PrimalDualHybridGradient(qp, params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, -34.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({-1, 8, 1, 2.5}, 1.0e-7));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({-2.0, 0.0, 2.375, 2.0 / 3}, 1.0e-7));
}
TEST_P(PrimalDualHybridGradientLPTest, InfeasiblePrimal) {
// This value for `iteration_upperbound` is particularly necessary for
// Malistsky and Pock. The adaptive rule detects infeasibility in less than
// 500 iterations.
const int iteration_upperbound = 2000;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(5);
params.mutable_termination_criteria()->set_eps_primal_infeasible(1.0e-6);
SolverResult output =
PrimalDualHybridGradient(SmallPrimalInfeasibleLp(), params);
EXPECT_EQ(output.solve_log.termination_reason(),
TERMINATION_REASON_PRIMAL_INFEASIBLE);
const auto& dual = output.dual_solution;
// The following two conditions check if the certificate is correct. For this
// problem the set of infeasibility certificates is equal to all the rays of
// the form -alpha * (1, 1) with alpha positive.
EXPECT_THAT(dual[0] / dual[1], DoubleNear(1, 1.0e-6));
EXPECT_LT(dual[1], 0.0);
// The reduced costs should be approximately zero. However, a small relative
// difference between `dual[0]` and `dual[1]` could translate to a large
// absolute difference, and hence large reduced costs. The following test uses
// the exact formula to make sure we're not adding the objective vector to the
// reduced costs.
EXPECT_THAT(
output.reduced_costs,
EigenArrayNear<double>({dual[1] - dual[0], dual[0] - dual[1]}, 1.0e-6));
EXPECT_LE(output.solve_log.iteration_count(), iteration_upperbound);
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 2);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 2);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 2);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 2);
}
TEST_P(PrimalDualHybridGradientLPTest, InfeasibleDual) {
const int iteration_upperbound = 500;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(5);
SolverResult output =
PrimalDualHybridGradient(SmallDualInfeasibleLp(), params);
EXPECT_EQ(output.solve_log.termination_reason(),
TERMINATION_REASON_DUAL_INFEASIBLE);
// The following two conditions check if the certificate is correct. For this
// problem the set of infeasibility certificates is equal to all the rays of
// the form alpha * (1, 1) with alpha positive.
EXPECT_THAT(output.primal_solution[0] / output.primal_solution[1],
DoubleNear(1, 1.0e-6));
EXPECT_GT(output.primal_solution[1], 0.0);
EXPECT_LE(output.solve_log.iteration_count(), iteration_upperbound);
}
TEST_P(PrimalDualHybridGradientLPTest, InfeasiblePrimalDual) {
const int iteration_upperbound = 600;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
// Adaptive restarts are disabled because they unexpectedly perform worse on
// this instance.
params.set_restart_strategy(PrimalDualHybridGradientParams::NO_RESTARTS);
params.set_major_iteration_frequency(5);
SolverResult output =
PrimalDualHybridGradient(SmallPrimalDualInfeasibleLp(), params);
EXPECT_THAT(output.solve_log.termination_reason(),
AnyOf(Eq(TERMINATION_REASON_DUAL_INFEASIBLE),
Eq(TERMINATION_REASON_PRIMAL_INFEASIBLE)));
EXPECT_LE(output.solve_log.iteration_count(), iteration_upperbound);
}
TEST_P(PrimalDualHybridGradientDiagonalQPTest, DiagonalQp1) {
const int iteration_upperbound = 96;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(12);
SolverResult output = PrimalDualHybridGradient(TestDiagonalQp1(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 6.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({1.0, 0.0}, 1.0e-6));
EXPECT_THAT(output.dual_solution,
EigenArrayNear(Eigen::ArrayXd::Constant(1, -1.0), 1.0e-6));
EXPECT_THAT(output.reduced_costs, EigenArrayNear<double>({4.0, 0.0}, 1.0e-6));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 2);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 2);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 1);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_constraints(), 1);
}
TEST_P(PrimalDualHybridGradientDiagonalQPTest, DiagonalQp2) {
const int iteration_upperbound = 240;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(12);
SolverResult output = PrimalDualHybridGradient(TestDiagonalQp2(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, -5.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({3.0, 1.0}, 1.0e-6));
EXPECT_THAT(output.dual_solution, ElementsAre(DoubleNear(0.0, 1.0e-6)));
EXPECT_THAT(output.reduced_costs, EigenArrayNear<double>({0.0, 0.0}, 1.0e-6));
}
TEST_P(PrimalDualHybridGradientDiagonalQPTest, DiagonalQp3) {
const int iteration_upperbound = 300;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(15);
SolverResult output = PrimalDualHybridGradient(TestDiagonalQp3(), params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 2.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({2.0, 0.0, 1.0}, 1.0e-6));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({-1.0, 1.0}, 1.0e-6));
EXPECT_THAT(output.reduced_costs, EigenArrayNear<double>({0, 0, 0}, 1.0e-6));
}
// This is like `DiagonalQp1` except it starts with a near-optimal solution and
// uses a shorter iteration limit.
TEST_P(PrimalDualHybridGradientDiagonalQPTest, QpWarmStart) {
const int iteration_upperbound = 35;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
params.set_major_iteration_frequency(5);
// Disable primal weight updating. In a warm-start situation, the primal
// weight should be carried over. In this test, the initial primal weight of 1
// is reasonable because the distance from the starting point to the primal
// and dual optimal solutions are about the same.
params.set_primal_weight_update_smoothing(0.0);
const PrimalAndDualSolution initial_solution = {
.primal_solution = Eigen::VectorXd{{0.999, 0.001}},
.dual_solution = Eigen::VectorXd{{-0.999}},
};
SolverResult output = PrimalDualHybridGradient(TestDiagonalQp1(), params,
std::move(initial_solution));
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 6.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({1.0, 0.0}, 1.0e-6));
EXPECT_THAT(output.dual_solution,
EigenArrayNear(Eigen::ArrayXd::Constant(1, -1.0), 1.0e-6));
EXPECT_THAT(output.reduced_costs, EigenArrayNear<double>({4.0, 0.0}, 1.0e-6));
}
// Tests an LP with no constraints.
TEST_P(PrimalDualHybridGradientLPTest, LpWithoutConstraints) {
const int iteration_upperbound = 2;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
QuadraticProgram qp(3, 0);
qp.variable_lower_bounds = Eigen::VectorXd{{-1, -kInfinity, -2}};
qp.variable_upper_bounds = Eigen::VectorXd{{kInfinity, 4, 10}};
qp.objective_vector = Eigen::VectorXd{{1, -1, 2}};
SolverResult output = PrimalDualHybridGradient(qp, params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, -9.0, 1.0e-6);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({-1, 4, -2}, 1.0e-6));
EXPECT_THAT(output.dual_solution, SizeIs(0));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 3);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 3);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 0);
EXPECT_EQ(output.solve_log.preprocessed_problem_stats().num_constraints(), 0);
}
// Tests an LP with no variables.
TEST_P(PrimalDualHybridGradientLPTest, LpWithoutVariables) {
const int iteration_upperbound = 2;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
QuadraticProgram qp(0, 3);
qp.constraint_lower_bounds = Eigen::VectorXd{{-1, -kInfinity, -2}};
qp.constraint_upper_bounds = Eigen::VectorXd{{kInfinity, 4, 10}};
SolverResult output = PrimalDualHybridGradient(qp, params);
VerifyTerminationReasonAndIterationCountForFixture(params, output);
VerifyObjectiveValues(output, 0.0, 1.0e-6);
EXPECT_THAT(output.primal_solution, SizeIs(0));
EXPECT_THAT(output.dual_solution, EigenArrayNear<double>({0, 0, 0}, 1.0e-6));
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 0);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 0);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 3);
EXPECT_EQ(output.solve_log.preprocessed_problem_stats().num_constraints(), 3);
}
TEST_P(PrimalDualHybridGradientLPTest, LpWithOnlyFixedVariable) {
const int iteration_upperbound = 2;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/0.0);
QuadraticProgram qp(1, 0);
qp.variable_lower_bounds = Eigen::VectorXd{{1}};
qp.variable_upper_bounds = Eigen::VectorXd{{1}};
qp.objective_vector = Eigen::VectorXd{{1}};
SolverResult output = PrimalDualHybridGradient(qp, params);
EXPECT_EQ(output.solve_log.termination_reason(), TERMINATION_REASON_OPTIMAL);
EXPECT_THAT(output.primal_solution,
EigenArrayNear(Eigen::ArrayXd::Constant(1, 1.0), 1.0e-6));
EXPECT_THAT(output.dual_solution, testing::SizeIs(0));
EXPECT_LE(output.solve_log.iteration_count(), iteration_upperbound);
}
TEST_P(PrimalDualHybridGradientLPTest, InfeasibleLpWithoutVariables) {
const int iteration_upperbound = 2;
PrimalDualHybridGradientParams params =
CreateSolverParamsForFixture(iteration_upperbound,
/*eps_optimal_absolute=*/1.0e-6);
QuadraticProgram qp(0, 1);
qp.constraint_lower_bounds = Eigen::VectorXd{{-1}};
qp.constraint_upper_bounds = Eigen::VectorXd{{-1}};
SolverResult output = PrimalDualHybridGradient(qp, params);
EXPECT_EQ(output.solve_log.termination_reason(),
TERMINATION_REASON_PRIMAL_INFEASIBLE);
EXPECT_THAT(output.primal_solution, SizeIs(0));
EXPECT_LT(output.dual_solution[0], 0.0);
EXPECT_EQ(output.solve_log.original_problem_stats().num_variables(), 0);
EXPECT_LE(output.solve_log.preprocessed_problem_stats().num_variables(), 0);
EXPECT_EQ(output.solve_log.original_problem_stats().num_constraints(), 1);
EXPECT_EQ(output.solve_log.preprocessed_problem_stats().num_constraints(), 1);
}
PrimalDualHybridGradientParams ParamsWithNoLimits() {
PrimalDualHybridGradientParams params;
// This disables the termination limits. A termination criteria must be set
// for the solver to terminate.
params.mutable_termination_criteria()
->mutable_simple_optimality_criteria()
->set_eps_optimal_relative(0.0);
params.mutable_termination_criteria()
->mutable_simple_optimality_criteria()
->set_eps_optimal_absolute(0.0);
params.set_record_iteration_stats(true);
return params;
}
TEST(PrimalDualHybridGradientTest, ClearsRunningAverage) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_termination_check_frequency(1);
params.set_major_iteration_frequency(major_iteration_frequency);
params.set_restart_strategy(PrimalDualHybridGradientParams::NO_RESTARTS);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_EQ(output.solve_log.iteration_count(), iteration_limit);
// The first entry in `iteration_stats` corresponds to the starting point.
ASSERT_EQ(output.solve_log.iteration_stats_size(), iteration_limit + 1);
for (int i = 0; i < output.solve_log.iteration_stats_size(); ++i) {
const auto& stats = output.solve_log.iteration_stats(i);
const int iterations_completed = stats.iteration_number();
EXPECT_EQ(iterations_completed, i);
if (iterations_completed == 0) {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART);
} else if (iterations_completed % major_iteration_frequency == 0) {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_WEIGHTED_AVERAGE_RESET)
<< "iteration = " << i;
} else {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART)
<< "iteration = " << i;
}
}
}
TEST(PrimalDualHybridGradientTest, RestartsEveryMajorIteration) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_termination_check_frequency(1);
params.set_major_iteration_frequency(major_iteration_frequency);
params.set_restart_strategy(
PrimalDualHybridGradientParams::EVERY_MAJOR_ITERATION);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_EQ(output.solve_log.iteration_count(), iteration_limit);
// The first entry in `iteration_stats` corresponds to the starting point.
ASSERT_EQ(output.solve_log.iteration_stats_size(), iteration_limit + 1);
for (int i = 0; i < output.solve_log.iteration_stats_size(); ++i) {
const auto& stats = output.solve_log.iteration_stats(i);
const int iterations_completed = stats.iteration_number();
EXPECT_EQ(iterations_completed, i);
if (iterations_completed == 0) {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART);
} else if (iterations_completed % major_iteration_frequency == 0) {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_RESTART_TO_AVERAGE)
<< "iteration = " << i;
} else {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART)
<< "iteration = " << i;
}
}
}
TEST(PrimalDualHybridGradientTest, SolveLogIncludesNameForNamedQP) {
PrimalDualHybridGradientParams params;
params.mutable_termination_criteria()->set_iteration_limit(1);
QuadraticProgram test_lp = TestLp();
test_lp.problem_name = "Test LP";
SolverResult output = PrimalDualHybridGradient(test_lp, params);
EXPECT_EQ(output.solve_log.instance_name(), "Test LP");
}
TEST(PrimalDualHybridGradientTest, SolveLogOmitsNameForUnnamedQP) {
PrimalDualHybridGradientParams params;
params.mutable_termination_criteria()->set_iteration_limit(1);
QuadraticProgram unnamed_test_lp = TestLp();
SolverResult output = PrimalDualHybridGradient(unnamed_test_lp, params);
EXPECT_FALSE(output.solve_log.has_instance_name());
}
TEST(PrimalDualHybridGradientTest, SolveLogIncludesParameters) {
PrimalDualHybridGradientParams params;
params.mutable_termination_criteria()->set_iteration_limit(1);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
EXPECT_EQ(output.solve_log.params().termination_criteria().iteration_limit(),
1);
}
TEST(PrimalDualHybridGradientTest, AdaptiveDistanceBasedRestartsWorkOnTestLp) {
PrimalDualHybridGradientParams params;
params.set_major_iteration_frequency(16);
params.mutable_termination_criteria()->set_iteration_limit(128);
params.set_restart_strategy(
PrimalDualHybridGradientParams::ADAPTIVE_DISTANCE_BASED);
// Low restart threshold.
params.set_necessary_reduction_for_restart(0.99);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
EXPECT_EQ(output.solve_log.termination_reason(), TERMINATION_REASON_OPTIMAL);
EXPECT_THAT(output.primal_solution,
EigenArrayNear<double>({-1, 8, 1, 2.5}, 1.0e-4));
EXPECT_THAT(output.dual_solution,
EigenArrayNear<double>({-2, 0, 2.375, 2.0 / 3}, 1.0e-4));
const auto convergence_info = GetConvergenceInformation(
output.solve_log.solution_stats(), output.solve_log.solution_type());
ASSERT_TRUE(convergence_info.has_value());
EXPECT_THAT(convergence_info->primal_objective(), DoubleNear(-34.0, 1.0e-4));
EXPECT_THAT(convergence_info->dual_objective(), DoubleNear(-34.0, 1.0e-4));
}
TEST(PrimalDualHybridGradientTest, AdaptiveDistanceBasedRestartsWorkOnTestQp) {
PrimalDualHybridGradientParams params;
params.set_major_iteration_frequency(16);
params.mutable_termination_criteria()->set_iteration_limit(128);
params.set_restart_strategy(
PrimalDualHybridGradientParams::ADAPTIVE_DISTANCE_BASED);
// Low restart threshold.
params.set_necessary_reduction_for_restart(0.99);
SolverResult output = PrimalDualHybridGradient(TestDiagonalQp1(), params);
EXPECT_EQ(output.solve_log.termination_reason(), TERMINATION_REASON_OPTIMAL);
}
TEST(PrimalDualHybridGradientTest, AdaptiveDistanceBasedRestartsToAverage) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 13;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_termination_check_frequency(1);
params.set_major_iteration_frequency(major_iteration_frequency);
params.set_restart_strategy(
PrimalDualHybridGradientParams::ADAPTIVE_DISTANCE_BASED);
params.set_necessary_reduction_for_restart(0.75);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_EQ(output.solve_log.iteration_count(), iteration_limit);
// The first entry in `iteration_stats` corresponds to the starting point.
ASSERT_EQ(output.solve_log.iteration_stats_size(), iteration_limit + 1);
for (int i = 0; i < output.solve_log.iteration_stats_size(); ++i) {
const auto& stats = output.solve_log.iteration_stats(i);
const int iterations_completed = stats.iteration_number();
EXPECT_EQ(iterations_completed, i);
if (iterations_completed == 0) {
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART);
} else if (iterations_completed == major_iteration_frequency) {
// An explicit restart should be triggered at the end of the first major
// iteration.
EXPECT_THAT(stats.restart_used(),
AnyOf(RESTART_CHOICE_RESTART_TO_AVERAGE,
RESTART_CHOICE_WEIGHTED_AVERAGE_RESET))
<< "iteration = " << i;
} else if (iterations_completed % major_iteration_frequency != 0) {
// No restarts should happen outside major iterations.
EXPECT_EQ(stats.restart_used(), RESTART_CHOICE_NO_RESTART);
}
}
}
TEST(PrimalDualHybridGradientTest, PrimalWeightFrozen) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
const double initial_primal_weight = 1.5;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_major_iteration_frequency(major_iteration_frequency);
params.set_restart_strategy(
PrimalDualHybridGradientParams::EVERY_MAJOR_ITERATION);
params.set_initial_primal_weight(initial_primal_weight);
params.set_primal_weight_update_smoothing(0.0);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
for (const auto& stats : output.solve_log.iteration_stats()) {
EXPECT_EQ(stats.primal_weight(), initial_primal_weight)
<< "iteration = " << stats.iteration_number();
}
}
TEST(PrimalDualHybridGradientTest, ConstantStepSize) {
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_termination_check_frequency(1);
params.set_linesearch_rule(
PrimalDualHybridGradientParams::CONSTANT_STEP_SIZE_RULE);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_FALSE(output.solve_log.iteration_stats().empty());
const double initial_step_size =
output.solve_log.iteration_stats(0).step_size();
for (const auto& stats : output.solve_log.iteration_stats()) {
EXPECT_EQ(stats.step_size(), initial_step_size)
<< "iteration = " << stats.iteration_number();
}
}
TEST(PrimalDualHybridGradientTest, StepSizeScaling) {
const int iteration_limit = 1;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_termination_check_frequency(1);
params.set_linesearch_rule(
PrimalDualHybridGradientParams::CONSTANT_STEP_SIZE_RULE);
SolverResult unscaled_output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_FALSE(unscaled_output.solve_log.iteration_stats().empty());
const double initial_step_size =
unscaled_output.solve_log.iteration_stats(0).step_size();
const double kStepSizeScaling = 0.5;
params.set_initial_step_size_scaling(kStepSizeScaling);
SolverResult scaled_output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_FALSE(scaled_output.solve_log.iteration_stats().empty());
EXPECT_EQ(scaled_output.solve_log.iteration_stats(0).step_size(),
initial_step_size * kStepSizeScaling);
}
// This verifies that `kkt_matrix_pass_limit` is checked every iteration.
TEST(PrimalDualHybridGradientTest, KktMatrixPassTermination) {
const int kkt_matrix_pass_limit = 13;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.mutable_termination_criteria()->set_kkt_matrix_pass_limit(
kkt_matrix_pass_limit);
params.set_linesearch_rule(
PrimalDualHybridGradientParams::CONSTANT_STEP_SIZE_RULE);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
ASSERT_FALSE(output.solve_log.iteration_stats().empty());
EXPECT_EQ(output.solve_log.termination_reason(),
TERMINATION_REASON_KKT_MATRIX_PASS_LIMIT);
EXPECT_EQ(output.solve_log.solution_stats().cumulative_kkt_matrix_passes(),
kkt_matrix_pass_limit);
}
TEST(PrimalDualHybridGradientTest,
StatsAtEachIterationWithRecordIterationStatsOn) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.set_record_iteration_stats(true);
// This is required for `ConvergenceInformation`, `InfeasibilityInformation`,
// and `PointMetadata` to be generated on each iteration.
params.set_termination_check_frequency(1);
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_major_iteration_frequency(major_iteration_frequency);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
EXPECT_EQ(output.solve_log.iteration_stats().size(), iteration_limit + 1);
for (const auto& stats : output.solve_log.iteration_stats()) {
EXPECT_NE(GetConvergenceInformation(stats, POINT_TYPE_CURRENT_ITERATE),
std::nullopt);
EXPECT_NE(GetInfeasibilityInformation(stats, POINT_TYPE_CURRENT_ITERATE),
std::nullopt);
EXPECT_NE(GetPointMetadata(stats, POINT_TYPE_CURRENT_ITERATE),
std::nullopt);
if (stats.iteration_number() > 0) {
EXPECT_NE(GetConvergenceInformation(stats, POINT_TYPE_AVERAGE_ITERATE),
std::nullopt);
EXPECT_NE(GetInfeasibilityInformation(stats, POINT_TYPE_AVERAGE_ITERATE),
std::nullopt);
EXPECT_NE(GetPointMetadata(stats, POINT_TYPE_AVERAGE_ITERATE),
std::nullopt);
EXPECT_NE(
GetInfeasibilityInformation(stats, POINT_TYPE_ITERATE_DIFFERENCE),
std::nullopt);
EXPECT_NE(GetPointMetadata(stats, POINT_TYPE_ITERATE_DIFFERENCE),
std::nullopt);
}
}
}
TEST(PrimalDualHybridGradientTest,
NoIterationStatsWithRecordIterationStatsOff) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.set_record_iteration_stats(false);
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_major_iteration_frequency(major_iteration_frequency);
// Random projection seeds should have no effect when `record_iteration_stats`
// is false.
params.add_random_projection_seeds(1);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
EXPECT_EQ(output.solve_log.iteration_stats().size(), 0);
}
TEST(PrimalDualHybridGradientTest, NoRandomProjectionsIfNotRequested) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.set_record_iteration_stats(true);
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);
params.set_major_iteration_frequency(major_iteration_frequency);
params.set_termination_check_frequency(1);
SolverResult output = PrimalDualHybridGradient(TestLp(), params);
EXPECT_EQ(output.solve_log.iteration_stats().size(), iteration_limit + 1);
for (const auto& stats : output.solve_log.iteration_stats()) {
EXPECT_THAT(stats.point_metadata(), Not(IsEmpty()));
for (const auto& metadata : stats.point_metadata()) {
EXPECT_THAT(metadata.random_primal_projections(), IsEmpty());
EXPECT_THAT(metadata.random_dual_projections(), IsEmpty());
}
}
}
TEST(PrimalDualHybridGradientTest, HasRandomProjectionsIfRequested) {
// An arbitrarily chosen major iteration frequency.
const int major_iteration_frequency = 17;
const int iteration_limit = 100;
PrimalDualHybridGradientParams params = ParamsWithNoLimits();
params.set_record_iteration_stats(true);
params.mutable_termination_criteria()->set_iteration_limit(iteration_limit);