This repository was archived by the owner on Nov 19, 2020. It is now read-only.
This repository was archived by the owner on Nov 19, 2020. It is now read-only.
AugmentedLagrangian hangs on linear problem #619
Description
In release 3.5.0, an update was made to the AugmentedLagrangian class in order to fix Issue #431. This fix works perfectly, in the sense that the failing unit test given in #431 now passes.
However, the update seems to have introduced a different problem. See below for a demonstration. In words, I'm considering the problem of minimizing 3x_0 - 4x_1 over the set of elements (x_0,x_1) in [0, 1] x [0, 1] summing to one, i.e. x_0 + x_1 = 1, corresponding to a line segment. As the mapping increases as x_0 increases and decreases as x_1 increases, the solution is (0.0, 1.0). However, when I construct the problem and run the algorithm, the unit tests hangs.
Here's a test snippet demonstrating the issue:
[TestMethod]
public void AugmentedLagrangianSolverTest03()
{
// Ensure that the Accord.NET random generator starts from a particular fixed seed.
Accord.Math.Random.Generator.Seed = 0;
// This problem is about minimizing $3x_0 - 4x_1$ over the elements of $[0, 1] \times[0, 1]$ summing to one.
var f = new NonlinearObjectiveFunction(2,
function: (x) => 3.0 * x[0] - 4.0 * x[1],
gradient: (x) => new[] { 3.0, -4.0 });
var constraints = new List<NonlinearConstraint>();
// Add the constraint $x_0 \ge 0$.
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[0],
gradient: (x) => new[] { 1.0, 0.0 },
shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0));
// Add the constraint $x_0 \le 1$.
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[0],
gradient: (x) => new[] { 1.0, 0.0 },
shouldBe: ConstraintType.LesserThanOrEqualTo, value: 1));
// Add the constraint $x_1 \ge 0$.
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[1],
gradient: (x) => new[] { 0.0, 1.0 },
shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0));
// Add the constraint $x_1 \le 1$.
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[1],
gradient: (x) => new[] { 0.0, 1.0 },
shouldBe: ConstraintType.LesserThanOrEqualTo, value: 1));
// Add the constraint $x_0 + x_1 = 1$.
constraints.Add(new NonlinearConstraint(f,
function: (x) => x[0] + x[1],
gradient: (x) => new[] { 1.0, 1.0 },
shouldBe: ConstraintType.EqualTo, value: 1));
var solver = new AugmentedLagrangian(f, constraints);
Assert.IsTrue(solver.Minimize());
double minValue = solver.Value;
Assert.IsFalse(Double.IsNaN(minValue));
// The solution is $(0.0, 1.0)$.
Assert.AreEqual(0.0, solver.Solution[0], 1e-5);
Assert.AreEqual(1.0, solver.Solution[1], 1e-5);
}