298 lines
6.7 KiB
C++
298 lines
6.7 KiB
C++
/**
|
|
* @file testConstraintOptimizer.cpp
|
|
* @brief Tests the optimization engine for SQP and BFGS Quadratic programming techniques
|
|
* @author Alex Cunningham
|
|
*/
|
|
|
|
#include <iostream>
|
|
#include <limits>
|
|
|
|
#include <boost/tuple/tuple.hpp>
|
|
#include <boost/optional.hpp>
|
|
|
|
#include <CppUnitLite/TestHarness.h>
|
|
|
|
#include <ConstraintOptimizer.h>
|
|
#include <smallExample.h>
|
|
|
|
using namespace std;
|
|
using namespace gtsam;
|
|
using namespace example;
|
|
|
|
/* ************************************************************************* */
|
|
// Example of a single Constrained QP problem from the matlab testCQP.m file.
|
|
TEST( matrix, CQP_example ) {
|
|
|
|
Matrix A = Matrix_(3, 2,
|
|
-1.0, -1.0,
|
|
-2.0, 1.0,
|
|
1.0, -1.0);
|
|
Matrix At = trans(A),
|
|
B = 2.0 * eye(3,3);
|
|
|
|
Vector b = Vector_(2, 4.0, -2.0),
|
|
g = zero(3);
|
|
|
|
Matrix G = zeros(5,5);
|
|
insertSub(G, B, 0, 0);
|
|
insertSub(G, A, 0, 3);
|
|
insertSub(G, At, 3, 0);
|
|
|
|
Vector rhs = zero(5);
|
|
subInsert(rhs, -1.0*g, 0);
|
|
subInsert(rhs, -1.0*b, 3);
|
|
|
|
// solve the system with the LDL solver
|
|
Vector actualFull = solve_ldl(G, rhs);
|
|
Vector actual = sub(actualFull, 0, 3);
|
|
|
|
Vector expected = Vector_(3, 2.0/7.0, 10.0/7.0, -6.0/7.0);
|
|
|
|
CHECK(assert_equal(expected, actual));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, CQP_example_automatic ) {
|
|
|
|
Matrix A = Matrix_(3, 2,
|
|
-1.0, -1.0,
|
|
-2.0, 1.0,
|
|
1.0, -1.0);
|
|
Matrix At = trans(A),
|
|
B = 2.0 * eye(3,3);
|
|
|
|
Vector g = zero(3),
|
|
h = Vector_(2, 4.0, -2.0);
|
|
|
|
Vector actState, actLam;
|
|
boost::tie(actState, actLam) = solveCQP(B, A, g, h);
|
|
|
|
Vector expected = Vector_(3, 2.0/7.0, 10.0/7.0, -6.0/7.0);
|
|
|
|
CHECK(assert_equal(expected, actState));
|
|
CHECK(actLam.size() == 2);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
|
|
/** SQP example from SQP tutorial */
|
|
namespace sqp_example1 {
|
|
|
|
/**
|
|
* objective function with gradient and hessian
|
|
* fx = (x2-2)^2 + x1^2;
|
|
*/
|
|
Vector objective(const Vector& x, boost::optional<Vector&> g = boost::none,
|
|
boost::optional<Matrix&> B = boost::none) {
|
|
double x1 = x(0), x2 = x(1);
|
|
if (g) *g = Vector_(2, 2.0*x1, 2.0*(x2-2.0));
|
|
if (B) *B = 2.0 * eye(2,2);
|
|
return Vector_(1, (x2-2)*(x2-2) + x1*x1);
|
|
}
|
|
|
|
/**
|
|
* constraint function with gradient and hessian
|
|
* cx = 4*x1^2 + x2^2 - 1;
|
|
*/
|
|
Vector constraint(const Vector& x, boost::optional<Matrix&> A = boost::none,
|
|
boost::optional<Matrix&> B = boost::none) {
|
|
double x1 = x(0), x2 = x(1);
|
|
if (A) *A = Matrix_(2,1, 8.0*x1, 2.0*x2);
|
|
if (B) *B = Matrix_(2,2,
|
|
8.0, 0.0,
|
|
0.0, 2.0);
|
|
return Vector_(1, 4.0*x1*x1 + x2*x2 - 1.0);
|
|
}
|
|
|
|
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, SQP_simple_analytic ) {
|
|
using namespace sqp_example1;
|
|
|
|
// parameters
|
|
double stepsize = 0.25;
|
|
size_t maxIt = 50;
|
|
|
|
// initial conditions
|
|
Vector x0 = Vector_(2, 2.0, 4.0),
|
|
lam0 = Vector_(1, -0.5);
|
|
|
|
// current state
|
|
Vector x = x0, lam = lam0;
|
|
|
|
for (size_t i =0; i<maxIt; ++i) {
|
|
|
|
// evaluate functions
|
|
Vector dfx;
|
|
Matrix dcx, ddfx, ddcx;
|
|
Vector fx = objective(x, dfx, ddfx);
|
|
Vector cx = constraint(x, dcx, ddcx);
|
|
|
|
// use analytic hessian
|
|
Matrix B = ddfx - lam(0)*ddcx;
|
|
|
|
// solve subproblem
|
|
Vector delta, lambda;
|
|
boost::tie(delta, lambda) = solveCQP(B, -dcx, dfx, -cx);
|
|
|
|
// update
|
|
Vector step = stepsize * delta;
|
|
x = x + step;
|
|
lam = lambda;
|
|
}
|
|
|
|
// verify
|
|
Vector expX = Vector_(2, 0.0, 1.0),
|
|
expLambda = Vector_(1, -1.0);
|
|
|
|
CHECK(assert_equal(expX, x, 1e-4));
|
|
CHECK(assert_equal(expLambda, lam, 1e-4));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, SQP_simple_manual_bfgs ) {
|
|
using namespace sqp_example1;
|
|
|
|
// parameters
|
|
double stepsize = 0.25;
|
|
size_t maxIt = 50;
|
|
|
|
// initial conditions
|
|
Vector x0 = Vector_(2, 2.0, 4.0),
|
|
lam0 = Vector_(1, -0.5);
|
|
|
|
// current state
|
|
Vector x = x0, lam = lam0;
|
|
Matrix Bi = eye(2,2);
|
|
Vector step, prev_dfx;
|
|
|
|
for (size_t i=0; i<maxIt; ++i) {
|
|
|
|
// evaluate functions
|
|
Vector dfx; Matrix dcx;
|
|
Vector fx = objective(x, dfx);
|
|
Vector cx = constraint(x, dcx);
|
|
|
|
// Just use dfx for the Hessian
|
|
if (i>0) {
|
|
Vector Bis = Bi * step,
|
|
y = dfx - prev_dfx;
|
|
Bi = Bi + outer_prod(y, y) / inner_prod(y, step)
|
|
- outer_prod(Bis, Bis) / inner_prod(step, Bis);
|
|
}
|
|
prev_dfx = dfx;
|
|
|
|
// solve subproblem
|
|
Vector delta, lambda;
|
|
boost::tie(delta, lambda) = solveCQP(Bi, -dcx, dfx, -cx);
|
|
|
|
// update
|
|
step = stepsize * delta;
|
|
x = x + step;
|
|
lam = lambda;
|
|
}
|
|
|
|
// verify
|
|
Vector expX = Vector_(2, 0.0, 1.0),
|
|
expLambda = Vector_(1, -1.0);
|
|
|
|
CHECK(assert_equal(expX, x, 1e-4));
|
|
CHECK(assert_equal(expLambda, lam, 1e-4));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, SQP_simple_bfgs ) {
|
|
using namespace sqp_example1;
|
|
|
|
// parameters
|
|
double stepsize = 0.25;
|
|
size_t maxIt = 50;
|
|
|
|
// initial conditions
|
|
Vector x0 = Vector_(2, 2.0, 4.0),
|
|
lam0 = Vector_(1, -0.5);
|
|
|
|
// create a BFGSEstimator
|
|
BFGSEstimator hessian(2);
|
|
|
|
// current state
|
|
Vector x = x0, lam = lam0;
|
|
Vector step;
|
|
|
|
for (size_t i=0; i<maxIt; ++i) {
|
|
|
|
// evaluate functions
|
|
Vector dfx; Matrix dcx;
|
|
Vector fx = objective(x, dfx);
|
|
Vector cx = constraint(x, dcx);
|
|
|
|
// Just use dfx for the Hessian
|
|
if (i>0) {
|
|
hessian.update(dfx, step);
|
|
} else {
|
|
hessian.update(dfx);
|
|
}
|
|
|
|
// solve subproblem
|
|
Vector delta, lambda;
|
|
boost::tie(delta, lambda) = solveCQP(hessian.getB(), -dcx, dfx, -cx);
|
|
|
|
// update
|
|
step = stepsize * delta;
|
|
x = x + step;
|
|
lam = lambda;
|
|
}
|
|
|
|
// verify
|
|
Vector expX = Vector_(2, 0.0, 1.0),
|
|
expLambda = Vector_(1, -1.0);
|
|
|
|
CHECK(assert_equal(expX, x, 1e-4));
|
|
CHECK(assert_equal(expLambda, lam, 1e-4));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, unconstrained_fg ) {
|
|
// create a graph
|
|
GaussianFactorGraph fg = createGaussianFactorGraph();
|
|
|
|
// parameters
|
|
size_t maxIt = 5;
|
|
double stepsize = 0.1;
|
|
|
|
// iterate to solve
|
|
VectorConfig x = createZeroDelta();
|
|
BFGSEstimator B(x.dim());
|
|
|
|
Vector step;
|
|
|
|
for (size_t i=0; i<maxIt; ++i) {
|
|
// find the gradient
|
|
Vector dfx = fg.gradient(x).vector();
|
|
|
|
// update hessian
|
|
if (i>0) {
|
|
B.update(dfx, step);
|
|
} else {
|
|
B.update(dfx);
|
|
}
|
|
|
|
// solve subproblem
|
|
Vector delta = solve_ldl(B.getB(), -dfx);
|
|
|
|
// update
|
|
step = stepsize * delta;
|
|
x = x.vectorUpdate(step);
|
|
}
|
|
|
|
// verify
|
|
VectorConfig expected = createCorrectDelta();
|
|
CHECK(assert_equal(expected,x));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
|
|
/* ************************************************************************* */
|