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58 changes: 29 additions & 29 deletions non-convex.py
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Original file line number Diff line number Diff line change
Expand Up @@ -63,7 +63,7 @@ def interpolation(f, g, f_alpha, g_alpha, alpha, c2, strong_wolfe_alpha, iters=2
# https://github.com/tamland/non-linear-optimization
l = 0.0
h = 1.0
for i in xrange(iters):
for i in np.arange(iters):
if strong_wolfe_alpha(f, g, alpha, c2):
return alpha

Expand All @@ -83,13 +83,13 @@ def steepest_descent(f, grad, x0, iterations, error):
x = x0
x_old = x
c2 = 0.9
for i in xrange(iterations):
for i in np.arange(iterations):
pk = -grad(x)
alpha = step_length(f, grad, x, 1.0, pk, c2)
x = x + alpha * pk
if i % 10 == 0:
# print " iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, alpha, x, f(x))
print " iter={}, x={}, f(x)={}".format(i, x, f(x))
print(" iter={}, x={}, f(x)={}".format(i, x, f(x)))

if np.linalg.norm(x - x_old) < error:
break
Expand All @@ -101,13 +101,13 @@ def newton(f, g, H, x0, iterations, error):
x = x0
x_old = x
c2 = 0.9
for i in xrange(iterations):
for i in np.arange(iterations):
pk = -np.linalg.solve(H(x), g(x))
alpha = step_length(f, g, x, 1.0, pk, c2)
x = x + alpha * pk
if i % 50 == 0:
# print " iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, alpha, x, f(x))
print " iter={}, x={}, f(x)={}".format(i, x, f(x))
print(" iter={}, x={}, f(x)={}".format(i, x, f(x)))

if np.linalg.norm(x - x_old) < error:
break
Expand All @@ -123,7 +123,7 @@ def conjugate_gradient(f, g, x0, iterations, error):
gk = g(xk)
pk = -gk

for i in xrange(iterations):
for i in np.arange(iterations):
alpha = step_length(f, g, xk, 1.0, pk, c2)
xk1 = xk + alpha * pk
gk1 = g(xk1)
Expand All @@ -132,7 +132,7 @@ def conjugate_gradient(f, g, x0, iterations, error):

if i % 10 == 0:
# print " iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, alpha, xk, f(xk))
print " iter={}, x={}, f(x)={}".format(i, xk, f(xk))
print(" iter={}, x={}, f(x)={}".format(i, xk, f(xk)))

if np.linalg.norm(xk1 - xk) < error:
xk = xk1
Expand All @@ -151,7 +151,7 @@ def bfgs(f, g, x0, iterations, error):
I = np.identity(xk.size)
Hk = I

for i in xrange(iterations):
for i in np.arange(iterations):
# compute search direction
gk = g(xk)
pk = -Hk.dot(gk)
Expand All @@ -175,7 +175,7 @@ def bfgs(f, g, x0, iterations, error):

if i % 10 == 0:
# print " iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, alpha, xk, f(xk))
print " iter={}, x={}, f(x)={}".format(i, xk, f(xk))
print(" iter={}, x={}, f(x)={}".format(i, xk, f(xk)))

if np.linalg.norm(xk1 - xk) < error:
xk = xk1
Expand All @@ -201,7 +201,7 @@ def Hp(H0, p):
q = g(xk)
a = np.zeros(m_t)
b = np.zeros(m_t)
for i in reversed(xrange(m_t)):
for i in reversed(np.arange(m_t)):
s = sks[i]
y = yks[i]
rho_i = float(1.0 / y.T.dot(s))
Expand All @@ -210,7 +210,7 @@ def Hp(H0, p):

r = H0.dot(q)

for i in xrange(m_t):
for i in np.arange(m_t):
s = sks[i]
y = yks[i]
rho_i = float(1.0 / y.T.dot(s))
Expand All @@ -219,7 +219,7 @@ def Hp(H0, p):

return r

for i in xrange(iterations):
for i in np.arange(iterations):
# compute search direction
gk = g(xk)
pk = -Hp(I, gk)
Expand All @@ -245,8 +245,8 @@ def Hp(H0, p):
rho_k = float(1.0 / yk.dot(sk))

if i % 10 == 0:
print " iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, \
alpha, xk, f(xk))
print(" iter={}, grad={}, alpha={}, x={}, f(x)={}".format(i, pk, \
alpha, xk, f(xk)))

if np.linalg.norm(xk1 - xk) < error:
xk = xk1
Expand All @@ -262,42 +262,42 @@ def Hp(H0, p):
error = 1e-4
max_iterations = 1000

print '\n======= Steepest Descent ======\n'
print('\n======= Steepest Descent ======\n')
start = time.time()
x, n_iter = steepest_descent(rosenbrock, grad_rosen, x0,
iterations=max_iterations, error=error)
end = time.time()
print " Steepest Descent terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter)
print(" Steepest Descent terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter))

print '\n======= Conjugate Gradient Method ======\n'
print('\n======= Conjugate Gradient Method ======\n')
start = time.time()
x, n_iter = conjugate_gradient(rosenbrock, grad_rosen, x0,
iterations=max_iterations, error=error)
end = time.time()
print " Conjugate Gradient Method terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter)
print(" Conjugate Gradient Method terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter))

print '\n======= Newton\'s Method ======\n'
print('\n======= Newton\'s Method ======\n')
start = time.time()
x, n_iter = newton(rosenbrock, grad_rosen, hessian_rosen, x0,
iterations=max_iterations, error=error)
end = time.time()
print " Newton\'s Method terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}" \
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter)
print(" Newton\'s Method terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}" \
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter))

print '\n======= Broyden-Fletcher-Goldfarb-Shanno ======\n'
print('\n======= Broyden-Fletcher-Goldfarb-Shanno ======\n')
start = time.time()
x, n_iter = bfgs(rosenbrock, grad_rosen, x0,
iterations=max_iterations, error=error)
end = time.time()
print " BFGS terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter)
print(" BFGS terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter))

print '\n======= Limited memory Broyden-Fletcher-Goldfarb-Shanno ======\n'
print('\n======= Limited memory Broyden-Fletcher-Goldfarb-Shanno ======\n')
start = time.time()
x, n_iter = l_bfgs(rosenbrock, grad_rosen, x0,
iterations=max_iterations, error=error)
end = time.time()
print " l-BFGS terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter)
print(" l-BFGS terminated in {} iterations, x = {}, f(x) = {}, time elapsed {}, time per iter {}"\
.format(n_iter, x, rosenbrock(x), end - start, (end - start) / n_iter))