BrentOptimizer Class

Use the BrentOptimizer class to find a minimum or maximum of a function when the derivative of the objective function is not available or very expensive to calculate.

The ObjectiveFunction property must be set to a function of one variable that evaluates the objective function. The ExtremumType property specifies whether a maximum or a minimum of the objective function is requested.

The algorithm itself runs in two phases. In the bracketing phase, a search is made for an interval that is known to contain an extremum. This step is performed automatically when the algorithm is run. You can run it manually by calling one of the FindBracket()()()() methods. You can check the validity of a bracketing interval by inspecting the IsBracketValid property.

Once a bracketing interval has been found, the location phase begins. The exact location of the extremum is found by successively narrowing the bracketing interval. This phase always converges for continuous functions. The FindExtremum()()()() method performs the location phase, and returns the best approximation to the extremum. Alternatively, one of the FindMaximum(Func<(Of <<'(Double, Double>)>>), Double, Double) or FindMinimum(Func<(Of <<'(Double, Double>)>>), Double, Double) methods can be used. This has the advantage that the objective function as well as an initial guess can be supplied with the method call.

The Extremum property returns the best approximation to the extremum. The EstimatedError property returns the uncertainty of the extremum. The ValueAtExtremum property returns the value of the objective function at the extremum. The Status property is a AlgorithmStatus value that indicates the outcome of the algorithm. A value of Normal shows normal termination. A value of Divergent usually indicates that a bracketing interval could not be found.

Convergence is tested using a simple convergence test based on the uncertainty in the location of the approximate extremum. The SolutionTest property returns a SimpleConvergenceTest object that allows you to specify the desired Tolerance and specific ConvergenceCriterion.

The algorithm uses Brent's original algorithm. In each iteration of the location phase, either a Golden Section step is taken, or a new approximation is calculated using quadratic or cubic interpolation. This method is the most robust method available for optimization in one dimension.