Accord.Tests.Math.AugmentedLagrangianSolverTest.AugmentedLagrangianSolverConstructorTest2 C# (CSharp) Method

        public void AugmentedLagrangianSolverConstructorTest2()
        {
            // min 100(y-x*x)²+(1-x)²
            //
            // s.t.  x >= 0
            //       y >= 0
            //

            var f = new NonlinearObjectiveFunction(2,

                function: (x) => 100 * Math.Pow(x[1] - x[0] * x[0], 2) + Math.Pow(1 - x[0], 2),

                gradient: (x) => new[] 
                {
                    2.0 * (200.0 * Math.Pow(x[0], 3) - 200.0 * x[0] * x[1] + x[0] - 1), // df/dx
                    200 * (x[1] - x[0]*x[0])                                            // df/dy
                }

            );


            var constraints = new List<NonlinearConstraint>();

            constraints.Add(new NonlinearConstraint(f,

                function: (x) => x[0],
                gradient: (x) => new[] { 1.0, 0.0 },

                shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0
            ));

            constraints.Add(new NonlinearConstraint(f,

                function: (x) => x[1],
                gradient: (x) => new[] { 0.0, 1.0 },

                shouldBe: ConstraintType.GreaterThanOrEqualTo, value: 0
            ));

            var solver = new AugmentedLagrangian(f, constraints);

            Assert.IsTrue(solver.Minimize());
            double minValue = solver.Value;

            Assert.AreEqual(0, minValue, 1e-10);
            Assert.AreEqual(1, solver.Solution[0], 1e-5);
            Assert.AreEqual(1, solver.Solution[1], 1e-5);

            Assert.IsFalse(Double.IsNaN(minValue));
            Assert.IsFalse(Double.IsNaN(solver.Solution[0]));
            Assert.IsFalse(Double.IsNaN(solver.Solution[1]));

        }