-
Notifications
You must be signed in to change notification settings - Fork 1.2k
/
sos_examples.cc
152 lines (139 loc) · 6.67 KB
/
sos_examples.cc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
#include "drake/solvers/test/sos_examples.h"
#include <gtest/gtest.h>
#include "drake/common/test_utilities/symbolic_test_util.h"
namespace drake {
namespace solvers {
namespace {
void CheckSymmetricMatrixPSD(const Eigen::Ref<const Eigen::MatrixXd>& mat,
double tol) {
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigen_solver;
eigen_solver.compute(mat);
EXPECT_TRUE((eigen_solver.eigenvalues().array() >=
Eigen::ArrayXd::Constant(mat.rows(), -tol))
.all());
}
} // namespace
UnivariateQuarticSos::UnivariateQuarticSos() : prog_() {
auto x = prog_.NewIndeterminates<1>()(0);
p_ = symbolic::Monomial(x, 4) + 4 * symbolic::Monomial(x, 3) +
6 * symbolic::Monomial(x, 2) + 4 * symbolic::Monomial(x, 1) + 5;
std::tie(gram_, monomial_basis_) = prog_.AddSosConstraint(p_);
}
void UnivariateQuarticSos::CheckResult(const MathematicalProgramResult& result,
double tol) const {
EXPECT_TRUE(result.is_success());
const Eigen::MatrixXd gram_val = result.GetSolution(gram_);
EXPECT_TRUE(symbolic::test::PolynomialEqual(
p_, monomial_basis_.dot(gram_val * monomial_basis_), tol));
CheckSymmetricMatrixPSD(gram_val, tol);
}
BivariateQuarticSos::BivariateQuarticSos() : prog_() {
auto x = prog_.NewIndeterminates<1>()(0);
auto y = prog_.NewIndeterminates<1>()(0);
p_ = 2 * symbolic::Monomial(x, 4) + 5 * symbolic::Monomial(y, 4) -
2 * symbolic::Monomial(x, 2) * symbolic::Monomial(y, 2) +
2 * symbolic::Monomial(x, 3) * symbolic::Monomial(y, 1) +
2 * symbolic::Monomial(x, 1) + 2;
std::tie(gram_, monomial_basis_) = prog_.AddSosConstraint(p_);
}
void BivariateQuarticSos::CheckResult(const MathematicalProgramResult& result,
double tol) const {
EXPECT_TRUE(result.is_success());
const Eigen::MatrixXd gram_val = result.GetSolution(gram_);
EXPECT_TRUE(symbolic::test::PolynomialEqual(
p_, monomial_basis_.dot(gram_val * monomial_basis_), tol));
CheckSymmetricMatrixPSD(gram_val, tol);
}
SimpleSos1::SimpleSos1() : prog_{} {
a_ = prog_.NewContinuousVariables<1>("a")(0);
b_ = prog_.NewContinuousVariables<1>("b")(0);
x_ = prog_.NewIndeterminates<1>("x")(0);
prog_.AddLinearCost(-a_ - b_);
p1_ = symbolic::Monomial(x_, 4) + a_ * symbolic::Monomial(x_, 1) + 2 + b_;
std::tie(gram1_, monomial_basis1_) = prog_.AddSosConstraint(p1_);
p2_ = symbolic::Polynomial({{symbolic::Monomial(x_, 2), a_ - b_ + 1},
{symbolic::Monomial(x_, 1), 1},
{symbolic::Monomial(), 1}});
std::tie(gram2_, monomial_basis2_) = prog_.AddSosConstraint(p2_);
}
void SimpleSos1::CheckResult(const MathematicalProgramResult& result,
double tol) const {
EXPECT_TRUE(result.is_success());
const Eigen::MatrixXd gram1_val = result.GetSolution(gram1_);
const Eigen::MatrixXd gram2_val = result.GetSolution(gram2_);
EXPECT_TRUE(symbolic::test::PolynomialEqual(
result.GetSolution(p1_),
monomial_basis1_.dot(gram1_val * monomial_basis1_), tol));
EXPECT_TRUE(symbolic::test::PolynomialEqual(
result.GetSolution(p2_),
monomial_basis2_.dot(gram2_val * monomial_basis2_), tol));
CheckSymmetricMatrixPSD(gram1_val, tol);
CheckSymmetricMatrixPSD(gram2_val, tol);
}
MotzkinPolynomial::MotzkinPolynomial() : prog_{} {
x_ = prog_.NewIndeterminates<1>()(0);
y_ = prog_.NewIndeterminates<1>()(0);
m_ = symbolic::Polynomial({{symbolic::Monomial({{x_, 4}, {y_, 2}}), 1},
{symbolic::Monomial({{x_, 2}, {y_, 4}}), 1},
{symbolic::Monomial(), 1},
{symbolic::Monomial({{x_, 2}, {y_, 2}}), -3}});
r_ = prog_.NewFreePolynomial({x_, y_}, 2);
std::tie(gram1_, monomial_basis1_) = prog_.AddSosConstraint(
r_ - symbolic::Polynomial({{symbolic::Monomial(x_, 2), 1},
{symbolic::Monomial(y_, 2), 1}}));
std::tie(gram2_, monomial_basis2_) = prog_.AddSosConstraint(m_ * r_);
}
void MotzkinPolynomial::CheckResult(const MathematicalProgramResult& result,
double tol) const {
EXPECT_TRUE(result.is_success());
const symbolic::Polynomial m_result =
symbolic::Polynomial(result.GetSolution(m_.ToExpression()), {x_, y_});
const symbolic::Polynomial r_result =
symbolic::Polynomial(result.GetSolution(r_.ToExpression()), {x_, y_});
const Eigen::MatrixXd gram1_val = result.GetSolution(gram1_);
const Eigen::MatrixXd gram2_val = result.GetSolution(gram2_);
EXPECT_TRUE(symbolic::test::PolynomialEqual(
r_result - symbolic::Polynomial(x_ * x_ + y_ * y_, {x_, y_}),
monomial_basis1_.dot(gram1_val * monomial_basis1_), tol));
EXPECT_TRUE(symbolic::test::PolynomialEqual(
m_result * r_result, monomial_basis2_.dot(gram2_val * monomial_basis2_),
tol));
CheckSymmetricMatrixPSD(gram1_val, tol);
CheckSymmetricMatrixPSD(gram2_val, tol);
}
UnivariateNonnegative1::UnivariateNonnegative1() : prog_{} {
a_ = prog_.NewContinuousVariables<1>()(0);
b_ = prog_.NewContinuousVariables<1>()(0);
c_ = prog_.NewContinuousVariables<1>()(0);
x_ = prog_.NewIndeterminates<1>()(0);
p_ = symbolic::Polynomial({{symbolic::Monomial(x_, 4), 1},
{symbolic::Monomial(x_, 3), a_},
{symbolic::Monomial(x_, 2), b_},
{symbolic::Monomial(x_, 1), c_},
{symbolic::Monomial(), 1}});
prog_.AddLinearEqualityConstraint(2 + a_ + b_ + c_ == 1);
prog_.AddLinearCost(-a_ - b_ - c_);
std::tie(s_, gram_s_) = prog_.NewSosPolynomial({x_}, 4);
std::tie(t_, gram_t_) = prog_.NewSosPolynomial({x_}, 2);
prog_.AddEqualityConstraintBetweenPolynomials(p_, s_ + x_ * t_);
}
void UnivariateNonnegative1::CheckResult(
const MathematicalProgramResult& result, double tol) const {
EXPECT_TRUE(result.is_success());
const symbolic::Polynomial p_result =
symbolic::Polynomial(result.GetSolution(p_.ToExpression()), {x_});
const symbolic::Polynomial s_result =
symbolic::Polynomial(result.GetSolution(s_.ToExpression()), {x_});
const symbolic::Polynomial t_result =
symbolic::Polynomial(result.GetSolution(t_.ToExpression()), {x_});
EXPECT_TRUE(
symbolic::test::PolynomialEqual(p_result, s_result + x_ * t_result, tol));
const double a_val = result.GetSolution(a_);
const double b_val = result.GetSolution(b_);
const double c_val = result.GetSolution(c_);
EXPECT_NEAR(result.get_optimal_cost(), -a_val - b_val - c_val, tol);
CheckSymmetricMatrixPSD(result.GetSolution(gram_s_), tol);
CheckSymmetricMatrixPSD(result.GetSolution(gram_t_), tol);
}
} // namespace solvers
} // namespace drake