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+#
+# Following Leunberger and Ye, Linear and Nonlinear Progamming, 3rd ed. p367
+# "The gradient projection method"
+# applied to an equality constraint for a simplex.
+#
+# min f(x)
+# s.t. x >= 0, sum_i x = d
+#
+# FIXME: enforce the positivity constraint - a limit on the line search?
+#
+
+from numpy import *
+from scipy import *
+from linesearch import line_search
+# local copy of scipy's Amijo line_search - wasn't enforcing alpha max correctly
+import sys
+
+dims = 4
+
+def f(x):
+ fv = x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3] - 2*x[0] - 3*x[3]
+ # print 'evaluating f at', x, 'value', fv
+ return fv
+
+def g(x):
+ return array([2*x[0] - 2, 2*x[1], 2*x[2], 2*x[3]-3])
+
+def pg(x):
+ gv = g(x)
+ return gv - sum(gv) / dims
+
+x = ones(dims) / dims
+old_fval = None
+
+while True:
+ fv = f(x)
+ gv = g(x)
+ dv = pg(x)
+
+ print 'x', x, 'f', fv, 'g', gv, 'd', dv
+
+ if old_fval == None:
+ old_fval = fv + 0.1
+
+ # solve for maximum step size i.e. when positivity constraints kick in
+ # x - alpha d = 0 => alpha = x/d
+ amax = max(x/dv)
+ if amax < 1e-8: break
+
+ stuff = line_search(f, pg, x, -dv, dv, fv, old_fval, amax=amax)
+ alpha = stuff[0] # Nb. can avoid next evaluation of f,g,d using 'stuff'
+ if alpha < 1e-8: break
+ x -= alpha * dv
+
+ old_fval = fv