158 lines
3.8 KiB
C++
158 lines
3.8 KiB
C++
/**
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* @file testConstraintOptimizer.cpp
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* @brief Tests the optimization engine for SQP and BFGS Quadratic programming techniques
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* @author Alex Cunningham
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*/
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#include <CppUnitLite/TestHarness.h>
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#include <boost/tuple/tuple.hpp>
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#include <boost/optional.hpp>
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#include <ConstraintOptimizer.h>
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using namespace std;
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using namespace gtsam;
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/* ************************************************************************* */
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// Example of a single Constrained QP problem from the matlab testCQP.m file.
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TEST( matrix, CQP_example ) {
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Matrix A = Matrix_(3, 2,
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-1.0, -1.0,
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-2.0, 1.0,
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1.0, -1.0);
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Matrix At = trans(A),
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B = 2.0 * eye(3,3);
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Vector b = Vector_(2, 4.0, -2.0),
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g = zero(3);
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Matrix G = zeros(5,5);
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insertSub(G, B, 0, 0);
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insertSub(G, A, 0, 3);
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insertSub(G, At, 3, 0);
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Vector rhs = zero(5);
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subInsert(rhs, -1.0*g, 0);
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subInsert(rhs, -1.0*b, 3);
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// solve the system with the LDL solver
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Vector actualFull = solve_ldl(G, rhs);
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Vector actual = sub(actualFull, 0, 3);
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Vector expected = Vector_(3, 2.0/7.0, 10.0/7.0, -6.0/7.0);
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CHECK(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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TEST( matrix, CQP_example_automatic ) {
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Matrix A = Matrix_(3, 2,
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-1.0, -1.0,
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-2.0, 1.0,
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1.0, -1.0);
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Matrix At = trans(A),
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B = 2.0 * eye(3,3);
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Vector g = zero(3),
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h = Vector_(2, 4.0, -2.0);
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Vector actState, actLam;
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boost::tie(actState, actLam) = solveCQP(B, A, g, h);
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Vector expected = Vector_(3, 2.0/7.0, 10.0/7.0, -6.0/7.0);
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CHECK(assert_equal(expected, actState));
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CHECK(actLam.size() == 2);
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}
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/* ************************************************************************* */
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/** SQP example from SQP tutorial */
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namespace sqp_example1 {
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/**
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* objective function with gradient and hessian
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* fx = (x2-2)^2 + x1^2;
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*/
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Vector objective(const Vector& x, boost::optional<Vector&> g = boost::none,
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boost::optional<Matrix&> B = boost::none) {
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double x1 = x(0), x2 = x(1);
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if (g) *g = Vector_(2, 2.0*x1, 2.0*(x2-2.0));
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if (B) *B = 2.0 * eye(2,2);
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return Vector_(1, (x2-2)*(x2-2) + x1*x1);
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}
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/**
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* constraint function with gradient and hessian
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* cx = 4*x1^2 + x2^2 - 1;
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*/
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Vector constraint(const Vector& x, boost::optional<Matrix&> A = boost::none,
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boost::optional<Matrix&> B = boost::none) {
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double x1 = x(0), x2 = x(1);
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if (A) *A = Matrix_(2,1, 8.0*x1, 2.0*x2);
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if (B) *B = Matrix_(2,2,
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8.0, 0.0,
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0.0, 2.0);
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return Vector_(1, 4.0*x1*x1 + x2*x2 - 1.0);
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}
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}
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/* ************************************************************************* */
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TEST( matrix, SQP_simple_analytic ) {
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using namespace sqp_example1;
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// Problem:
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// min(x) f(x) = (x2-2)^2 + x1^2
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// s.t. c(x) = 4x1^2 + x2^2 - 1 =0
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// state is x = [x1 x2]' , with dim(state) = 2
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// constraint has dim p = 1
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// parameters
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double stepsize = 0.25;
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size_t maxIt = 50;
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// initial conditions
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Vector x0 = Vector_(2, 2.0, 4.0),
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lam0 = Vector_(1, -0.5);
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// current state
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Vector x = x0, lam = lam0;
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for (size_t i =0; i<maxIt; ++i) {
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// evaluate functions
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Vector dfx;
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Matrix dcx, ddfx, ddcx;
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Vector fx = objective(x, dfx, ddfx);
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Vector cx = constraint(x, dcx, ddcx);
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// use analytic hessian
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Matrix B = ddfx - lam(0)*ddcx;
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// solve subproblem
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Vector delta, lambda;
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boost::tie(delta, lambda) = solveCQP(B, -dcx, dfx, -cx);
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// update
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Vector step = stepsize * delta;
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x = x + step;
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lam = lambda;
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}
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// verify
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Vector expX = Vector_(2, 0.0, 1.0),
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expLambda = Vector_(1, -1.0);
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CHECK(assert_equal(expX, x, 1e-4));
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CHECK(assert_equal(expLambda, lam, 1e-4));
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}
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/* ************************************************************************* */
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int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
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/* ************************************************************************* */
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