Renamed QuadraticSubproblem to DogLegSubproblem.

src/Numerics/Optimization/ITrustRegionSubProblem.cs

@@ -5,7 +5,6 @@ namespace MathNet.Numerics.Optimization
     public interface ITrustRegionSubproblem
     {
         Vector<double> Pstep { get; }
-        double PredictedReduction { get; }
         bool HitBoundary { get; }
 
         void Solve(IObjectiveModel objective, double radius);

src/Numerics/Optimization/Subproblems/QuadraticSubproblem.cs → src/Numerics/Optimization/Subproblems/DogLegSubproblem.cs

@@ -2,12 +2,10 @@
 
 namespace MathNet.Numerics.Optimization.Subproblems
 {
-    internal class QuadraticSubproblem : ITrustRegionSubproblem
+    internal class DogLegSubproblem : ITrustRegionSubproblem
     {
         public Vector<double> Pstep { get; private set; }
 
-        public double PredictedReduction { get; private set; }
-
         public bool HitBoundary { get; private set; }
 
         public void Solve(IObjectiveModel objective, double delta)
@@ -32,14 +30,12 @@ namespace MathNet.Numerics.Optimization.Subproblems
                 // Pgn is inside trust region radius
                 HitBoundary = false;
                 Pstep = Pgn;
-                PredictedReduction = RSS;
             }
             else if (alpha * Psd.L2Norm() >= delta)
             {
                 // Psd is outside trust region radius
                 HitBoundary = true;
                 Pstep = delta / Psd.L2Norm() * Psd;
-                PredictedReduction = delta * (2.0 * (alpha * Gradient).L2Norm() - delta) / 2.0 / alpha;
             }
             else
             {
@@ -47,7 +43,6 @@ namespace MathNet.Numerics.Optimization.Subproblems
                 HitBoundary = true;
                 var beta = Util.FindBeta(alpha, Psd, Pgn, delta).Item2;
                 Pstep = alpha * Psd + beta * (Pgn - alpha * Psd);
-                PredictedReduction = 0.5 * alpha * (1 - beta) * (1 - beta) * Gradient.DotProduct(Gradient) + beta * (2 - beta) * RSS;
             }
         }
     }

src/Numerics/Optimization/Subproblems/Util.cs

@@ -26,7 +26,10 @@ namespace MathNet.Numerics.Optimization.Subproblems
             var beta1 = -aux / 2.0 / a;
             var beta2 = -2.0 * c / aux;
 
-            return new Tuple<double, double>(beta1, beta2);
+            // return sorted beta
+            return (beta1 < beta2)
+                ? new Tuple<double, double>(beta1, beta2)
+                : new Tuple<double, double>(beta2, beta1);
         }
     }
 }

src/Numerics/Optimization/TrustRegionDogLegMinimizer.cs

@@ -6,7 +6,7 @@ namespace MathNet.Numerics.Optimization
     public sealed class TrustRegionDogLegMinimizer : TrustRegionMinimizerBase
     {
         public TrustRegionDogLegMinimizer(double gradientTolerance = 1E-8, double stepTolerance = 1E-8, double functionTolerance = 1E-8, double radiusTolerance = 1E-8, int maximumIterations = -1)
-            : base(TrustRegionSubproblem.Quadratic(), gradientTolerance, stepTolerance, functionTolerance, radiusTolerance, maximumIterations)
+            : base(TrustRegionSubproblem.DogLeg(), gradientTolerance, stepTolerance, functionTolerance, radiusTolerance, maximumIterations)
         { }
     }
 }

src/Numerics/Optimization/TrustRegionMinimizerBase.cs

@@ -189,8 +189,9 @@ namespace MathNet.Numerics.Optimization
                 // solve the subproblem
                 subproblem.Solve(objective, delta);
                 var Pstep = subproblem.Pstep;
-                var predictedReduction = subproblem.PredictedReduction;
                 var hitBoundary = subproblem.HitBoundary;
+                // predicted reduction = L(0) - L(Δp) = Δp'g - 1/2 * Δp'HΔp
+                var predictedReduction = objective.Gradient.DotProduct(Pstep) - 0.5 * Pstep.DotProduct(objective.Hessian * Pstep);
 
                 if (Pstep.L2Norm() <= stepTolerance * (stepTolerance + P.L2Norm()))
                 {

src/Numerics/Optimization/TrustRegionSubProblem.cs

@@ -4,9 +4,9 @@ namespace MathNet.Numerics.Optimization
 {
     public static class TrustRegionSubproblem
     {
-        public static ITrustRegionSubproblem Quadratic()
+        public static ITrustRegionSubproblem DogLeg()
         {
-            return new QuadraticSubproblem();
+            return new DogLegSubproblem();
         }
     }
 }