/// <summary>Adds a specific inequality constraint.
/// </summary>
/// <param name="inequalityConstraintFunction">The inequality constraint function, i.e. a argument x will be accepted iff c(x) < <paramref name="tolerance"/> component-wise.</param>
/// <param name="constraintFunctionDimension"> The dimensionality of the constraint function.</param>
/// <param name="tolerance">An array of at least <paramref name="constraintFunctionDimension"/> elements that represents the tolerance in each constraint dimension; or <c>null</c> for zero tolerances.</param>
/// <returns>A value indicating whether the inequality constraint has been added.</returns>
public NLoptResultCode AddInequalityConstraint(NLoptVectorInequalityConstraintFunction inequalityConstraintFunction, int constraintFunctionDimension, double[] tolerance)
{
if (m_NLopPtr == IntPtr.Zero)
{
throw new ObjectDisposedException("NLoptPtr");
}
return(nlopt_add_inequality_mconstraint(m_NLopPtr, constraintFunctionDimension, inequalityConstraintFunction, IntPtr.Zero, tolerance));
}
/// <summary>Creates a new <see cref="NLoptConstraint"/> object.
/// </summary>
/// <param name="linearInequalityConstraint">The specific constraints in its <see cref="MultiDimRegion.LinearInequality"/> representation.</param>
/// <returns>A specific <see cref="NLoptConstraint"/> object with respect to the specified optimization algorithm.</returns>
/// <exception cref="InvalidOperationException">Thrown, if the optimization algorithm does not support this kind of constraints.</exception>
public NLoptConstraint Create(MultiDimRegion.LinearInequality linearInequalityConstraint)
{
if (linearInequalityConstraint == null)
{
throw new ArgumentNullException(nameof(linearInequalityConstraint));
}
if (nloptMultiDimOptimizer.Configuration.NonlinearConstraintRequirement.HasFlag(NLoptNonlinearConstraintRequirement.SupportsInequalityConstraints) == false)
{
throw new InvalidOperationException("The NLopt algorithm does not support linear inequality constraints");
}
var entriesOfA = new List <double>();
var entriesOfb = new List <double>();
int r = linearInequalityConstraint.GetRegionConstraints(entriesOfA, entriesOfb); // condition A^t * x >= b should be written as c(x) = b - A^t * x
var A = entriesOfA.ToArray(); // matrix A is of type d[dimension] x r, provided column-by-column
var b = entriesOfb.ToArray();
NLoptVectorInequalityConstraintFunction c = (m, result, n, x, grad, data) => // todo: bug in nlopt(?) - argument x has wrong dimension
{
BLAS.Level2.dgemv(n, m, -1.0, A, x, 0.0, result, BLAS.MatrixTransposeState.Transpose);
VectorUnit.Basics.Add(r, result, b);
if (grad != null)
{
/* it holds \partial c_i / \partial x_j = A[j,i] which should be stored in grad[i * n + j], i = 0,...,m-1, j = 0,...,n-1 */
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
grad[i * n + j] = A[j + i * n]; // can be improved
}
}
}
};
var tolerance = Enumerable.Repeat(MachineConsts.Epsilon, r).ToArray();
return(new NLoptConstraint(this,
linearInequalityConstraint.Dimension,
"Linear Inequality constraint",
nloptPtr =>
{
var code = nloptPtr.AddInequalityConstraint(c, r, tolerance);
if (code != NLoptResultCode.Success)
{
throw new InvalidOperationException(String.Format("Constraint can not be set to NLopt algorithm {0}; error code: {1}.", nloptPtr.ToString(), code));
}
},
infoOutputPackage => { }
));
}
private static extern NLoptResultCode nlopt_add_inequality_mconstraint(IntPtr opt, int m, [MarshalAs(UnmanagedType.FunctionPtr)] NLoptVectorInequalityConstraintFunction constraintFunction, IntPtr data, double[] tolerance);
/// <summary>Creates a new <see cref="NLoptConstraint"/> object.
/// </summary>
/// <param name="polynomialConstraint">The specific constraints in its <see cref="MultiDimRegion.Polynomial"/> representation.</param>
/// <returns>A specific <see cref="NLoptConstraint"/> object with respect to the specified optimization algorithm.</returns>
/// <exception cref="InvalidOperationException">Thrown, if the optimization algorithm does not support this kind of constraints.</exception>
public NLoptConstraint Create(MultiDimRegion.Polynomial polynomialConstraint)
{
if (polynomialConstraint == null)
{
throw new ArgumentNullException(nameof(polynomialConstraint));
}
if (nloptMultiDimOptimizer.Configuration.NonlinearConstraintRequirement.HasFlag(NLoptNonlinearConstraintRequirement.SupportsInequalityConstraints) == false)
{
throw new InvalidOperationException("The NLopt algorithm does not support linear inequality for polynomial constraints");
}
/* we split the constraint to at most two NLopt constraints c_1(x) <= \epsilon and c_2(x) <= \epsilon, where
* c_1(x) = P(x) - upper bound,
* c_2(x) = lower bound - P(x),
* where P(x) is the polynomial representation of the constraint.
*
* We use the NLopt vector constraint representation to combine both constraint, because the evaluation is almost identically.
*/
if ((Double.IsNegativeInfinity(polynomialConstraint.LowerBound) == false) && (Double.IsPositiveInfinity(polynomialConstraint.UpperBound) == false))
{
NLoptVectorInequalityConstraintFunction c = (m, result, n, x, grad, data) =>
{
double polynomialValue = 0.0;
foreach (var term in polynomialConstraint.Terms)
{
double temp = 0.0;
foreach (var monomial in term.Item2)
{
temp += DoMath.Pow(x[monomial.ArgumentIndex], monomial.Power);
}
polynomialValue += term.Item1 * temp;
}
if (grad != null)
{
for (int j = 0; j < n; j++)
{
grad[j] = 0.0;
}
foreach (var term in polynomialConstraint.Terms)
{
foreach (var monomial in term.Item2)
{
grad[monomial.ArgumentIndex] -= term.Item1 * monomial.Power * DoMath.Pow(x[monomial.ArgumentIndex], monomial.Power - 1);
}
}
}
result[0] = polynomialValue - polynomialConstraint.UpperBound;
result[1] = polynomialConstraint.LowerBound - polynomialValue;
};
var tolerance = new[] { MachineConsts.Epsilon, MachineConsts.Epsilon };
return(new NLoptConstraint(this,
polynomialConstraint.Dimension,
"Polynomial constraint",
nloptPtr =>
{
var code = nloptPtr.AddInequalityConstraint(c, 2, tolerance);
if (code != NLoptResultCode.Success)
{
throw new InvalidOperationException(String.Format("Constraint can not be set to NLopt algorithm {0}; error code: {1}.", nloptPtr.ToString(), code));
}
}
));
}
else if (Double.IsNegativeInfinity(polynomialConstraint.LowerBound) == false)
{
return(CreateSingle(polynomialConstraint, polynomialConstraint.LowerBound, sign: 1));
}
else
{
return(CreateSingle(polynomialConstraint, polynomialConstraint.UpperBound, sign: -1));
}
}
