Add absolute bracket width termination condition

optimization/optimizers/line_search/golden_section.h

@@ -10,8 +10,12 @@ namespace optimization {
 //--------------------------------------------------------------------------------------------------
 class GoldenSection {
 public:
-    // Note: This tolerance default is suitable for double precision floats.
-    GoldenSection(Scalar tolerance = 3e-8): tolerance_(tolerance), n_evaluations_(0) {}
+    // Note:
+    //   - the default absolute tolerance is equivalent to no absolute termination condition
+    //   - the default relative tolerance is suitable for double precision floats
+    GoldenSection(Scalar abs_tol = -1, Scalar rel_tol = 3e-8)
+        : abs_tol_(abs_tol), rel_tol_(rel_tol), n_evaluations_(0)
+    {}
 
     uint32_t n_evaluations() const { return n_evaluations_; }
 
@@ -19,7 +23,10 @@ public:
     Sample<Scalar> optimize(Objective const& objective, Bracket const& bracket);
 
 private:
-    Scalar tolerance_;
+    // Goal for absolute width of the bracket. Put a negative number if you want to abs tol.
+    Scalar abs_tol_;
+    // Goal for width of bracket relative to central value. Should always have this.
+    Scalar rel_tol_;
     uint32_t n_evaluations_;
 
     static constexpr Scalar golden_ratio_big_ = 0.618034;
@@ -65,7 +72,7 @@ Sample<Scalar> GoldenSection::optimize(Objective const& objective, Bracket const
 
     // Keep interpolating until our bracket is sufficiently tight.
     // See Numerical Recipes for the thought behind this particular test.
-    while (x_3 - x_0 > tolerance_ * (std::abs(x_1) + std::abs(x_2))) {
+    while (x_3 - x_0 > abs_tol_ && x_3 - x_0 > rel_tol_ * (std::abs(x_1) + std::abs(x_2))) {
         if (y_2 < y_1) {
             // x_1 is our new left edge; interpolate between x_2 and x_3
             shift(x_0, x_1, x_2, golden_ratio_big_ * x_2 + golden_ratio_small_ * x_3);