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csdp_test_examples.cc
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csdp_test_examples.cc
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#include "drake/solvers/test/csdp_test_examples.h"
#include <limits>
#include <vector>
namespace drake {
namespace solvers {
const double kInf = std::numeric_limits<double>::infinity();
SDPwithOverlappingVariables1::SDPwithOverlappingVariables1()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<3>()} {
prog_->AddLinearCost(2 * x_(0) + x_(2));
prog_->AddBoundingBoxConstraint(1, 1, x_(1));
prog_->AddBoundingBoxConstraint(0.5, kInf, x_(0));
prog_->AddBoundingBoxConstraint(-kInf, 2, x_(2));
prog_->AddPositiveSemidefiniteConstraint(
(Matrix2<symbolic::Variable>() << x_(0), x_(1), x_(1), x_(0)).finished());
prog_->AddPositiveSemidefiniteConstraint(
(Matrix2<symbolic::Variable>() << x_(0), x_(2), x_(2), x_(0)).finished());
}
SDPwithOverlappingVariables2::SDPwithOverlappingVariables2()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<2>()} {
prog_->AddLinearCost(2 * x_(0) + x_(1));
prog_->AddBoundingBoxConstraint(Eigen::Vector2d(2, 1),
Eigen::Vector2d(3, kInf), x_);
prog_->AddPositiveSemidefiniteConstraint(
(Matrix2<symbolic::Variable>() << x_(0), x_(1), x_(1), x_(0)).finished());
}
CsdpDocExample::CsdpDocExample()
: prog_{new MathematicalProgram()},
X1_{prog_->NewSymmetricContinuousVariables<2>()},
X2_{prog_->NewSymmetricContinuousVariables<3>()},
y_{prog_->NewContinuousVariables<2>()} {
prog_->AddPositiveSemidefiniteConstraint(X1_);
prog_->AddPositiveSemidefiniteConstraint(X2_);
prog_->AddBoundingBoxConstraint(Eigen::Vector2d(0, 0),
Eigen::Vector2d(kInf, kInf), y_);
prog_->AddLinearCost(-(2 * X1_(0, 0) + 2 * X1_(0, 1) + 2 * X1_(1, 1) +
3 * X2_(0, 0) + 2 * X2_(1, 1) + 2 * X2_(0, 2) +
3 * X2_(2, 2)));
prog_->AddLinearEqualityConstraint(
3 * X1_(0, 0) + 2 * X1_(0, 1) + 3 * X1_(1, 1) + y_(0), 1);
prog_->AddLinearEqualityConstraint(
3 * X2_(0, 0) + 4 * X2_(1, 1) + 2 * X2_(0, 2) + 5 * X2_(2, 2) + y_(1), 2);
}
LinearProgramBoundingBox1::LinearProgramBoundingBox1()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<8>()} {
Eigen::Matrix<double, 8, 1> lower, upper;
lower << 0, 0, -1, -kInf, -2, 0, 1, -kInf;
upper << kInf, 5, kInf, 10, 5, 0, 1, kInf;
prog_->AddBoundingBoxConstraint(lower, upper, x_);
prog_->AddLinearCost(-(-x_(0) + x_(1) - 2 * x_(2) + 3 * x_(3) + x_(4) + 1));
}
CsdpLinearProgram2::CsdpLinearProgram2()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<3>()} {
prog_->AddLinearEqualityConstraint(2 * x_(0) + 3 * x_(1) + x_(2), 1);
Eigen::Matrix<double, 4, 3> A;
// clang-format off
A << 1, 0, -2,
1, 2, 0,
-1, 0, 3,
1, 1, 4;
// clang-format on
Eigen::Vector4d lower(-kInf, -2, -2, 3);
Eigen::Vector4d upper(-1, kInf, 3, 3);
prog_->AddLinearConstraint(A, lower, upper, x_);
prog_->AddLinearCost(x_(0) + 2 * x_(1) + 3 * x_(2));
}
CsdpLinearProgram3::CsdpLinearProgram3()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<3>()} {
prog_->AddBoundingBoxConstraint(Eigen::Vector2d(-1, -kInf),
Eigen::Vector2d(10, 8), x_.head<2>());
Eigen::Matrix<double, 4, 3> A;
// clang-format off
A << 1, 2, 3,
2, 0, -1,
0, 1, -3,
1, 0, 1;
// clang-format on
prog_->AddLinearConstraint(A, Eigen::Vector4d(3, -1, -kInf, -4),
Eigen::Vector4d(3, kInf, 5, 9), x_);
prog_->AddLinearCost(-(2 * x_(0) + 3 * x_(1) + 4 * x_(2) + 3));
}
TrivialSDP1::TrivialSDP1()
: prog_{new MathematicalProgram()},
X1_{prog_->NewSymmetricContinuousVariables<3>()} {
prog_->AddPositiveSemidefiniteConstraint(X1_);
prog_->AddLinearEqualityConstraint(X1_(0, 0) + X1_(1, 1) + X1_(2, 2), 1);
prog_->AddLinearConstraint(X1_(0, 1) + X1_(1, 2) - 2 * X1_(0, 2), -kInf, 0);
prog_->AddLinearCost(-(X1_(0, 1) + X1_(1, 2)));
}
TrivialSDP2::TrivialSDP2()
: prog_{new MathematicalProgram()},
X1_{prog_->NewSymmetricContinuousVariables<2>()},
y_{prog_->NewContinuousVariables<1>()(0)} {
prog_->AddPositiveSemidefiniteConstraint(X1_);
Eigen::Matrix2d F0 = Eigen::Matrix2d::Identity();
Eigen::Matrix2d F1;
F1 << 1, 2, 2, 3;
Eigen::Matrix2d F2;
F2 << 2, 0, 0, 4;
prog_->AddConstraint(
std::make_shared<LinearMatrixInequalityConstraint>(
std::vector<Eigen::Ref<const Eigen::MatrixXd>>{F0, F1, F2}),
Vector2<symbolic::Variable>(y_, X1_(0, 0)));
prog_->AddLinearEqualityConstraint(X1_(0, 0) + 2 * X1_(1, 1) + 3 * y_, 1);
prog_->AddLinearCost(-y_);
}
TrivialSOCP1::TrivialSOCP1()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<3>()} {
prog_->AddBoundingBoxConstraint(Eigen::Vector2d::Zero(),
Eigen::Vector2d(kInf, kInf), x_.tail<2>());
prog_->AddLinearEqualityConstraint(x_(0) + x_(1) + x_(2), 10);
Eigen::Matrix3d A;
// clang-format off
A << 2, 0, 0,
0, 3, 0,
1, 0, 1;
// clang-format on
Eigen::Vector3d b(1, 2, 3);
prog_->AddLorentzConeConstraint(A, b, x_);
prog_->AddLinearCost(-x_(0));
}
TrivialSOCP2::TrivialSOCP2()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<2>()} {
prog_->AddLinearCost(-x_(1));
Eigen::Matrix<double, 3, 2> A;
// clang-format off
A << 1, 0,
1, 1,
1, -1;
// clang-format on
Eigen::Vector3d b(2, 1, 1);
prog_->AddLorentzConeConstraint(A, b, x_);
}
TrivialSOCP3::TrivialSOCP3()
: prog_{new MathematicalProgram()}, x_{prog_->NewContinuousVariables<2>()} {
prog_->AddLinearCost(x_(1));
Eigen::Matrix<double, 4, 2> A;
// clang-format off
A << 2, 0,
0, 3,
1, 0,
3, 1;
// clang-format on
Eigen::Vector4d b(2, 4, 2, 1);
prog_->AddRotatedLorentzConeConstraint(A, b, x_);
}
} // namespace solvers
} // namespace drake