adds doublewell objective

descent/objectives.py

@@ -4,7 +4,7 @@
 import numpy as np
 from functools import wraps
 
-__all__ = ['rosenbrock', 'sphere', 'matyas', 'beale', 'booth', 'mccormick',
+__all__ = ['doublewell', 'rosenbrock', 'sphere', 'matyas', 'beale', 'booth', 'mccormick',
            'camel', 'michalewicz', 'bohachevsky1', 'zakharov', 'dixon_price']
 
 
@@ -40,6 +40,17 @@ def param_init():
     return decorator
 
 
+@objective(xstar=(0,), param_scales=(10,))
+def doublewell(theta):
+    """Pointwise minimum of two quadratic bowls"""
+    k0, k1, depth = 0.01, 100, 0.5
+    shallow = 0.5 * k0 * theta ** 2 + depth
+    deep = 0.5 * k1 * theta ** 2
+    obj = np.minimum(shallow, deep)
+    grad = np.where(deep < shallow, k0 * theta, k1 * theta)
+    return obj, grad
+
+
 @objective(xstar=(1, 1))
 def rosenbrock(theta):
     """Objective and gradient for the rosenbrock function"""