Add constrained example

Author: mjhough

examples/rosenbrock_constrained.py

@@ -0,0 +1,31 @@
+# DFO-LS example: minimize the Rosenbrock function with arbitrary convex constraints
+from __future__ import print_function
+import numpy as np
+import dfols
+
+# Define the objective function
+def rosenbrock(x):
+    return np.array([10.0 * (x[1] - x[0] ** 2), 1.0 - x[0]])
+
+# Define the starting point
+x0 = np.array([-1.2, 1])
+
+def pball(x):
+    c = np.array([0.7,1.5]) # ball centre
+    r = 0.4 # ball radius
+    return c + (r/np.max([np.linalg.norm(x-c),r]))*(x-c)
+
+def pbox(x):
+    l = np.array([-2, 1.1]) # lower bound
+    u = np.array([0.9, 3]) # upper bound
+    return np.minimum(np.maximum(x,l), u)
+
+# For optional extra output details
+import logging
+logging.basicConfig(level=logging.DEBUG, format='%(message)s')
+
+# Call DFO-LS
+soln = dfols.solve(rosenbrock, x0, projections=[pball,pbox])
+
+# Display output
+print(soln)