From b794f878fef03ee0993ad6a48e159305806f47bd Mon Sep 17 00:00:00 2001
From: asilador <asilador@illinois.edu>
Date: Wed, 15 Feb 2017 10:45:56 -0600
Subject: [PATCH] Increased convergence speed by modifying armijo's rule to
include beta^m
---
Assignment 1/assignment1.py | 36 +++++++++++++++++++++---------------
1 file changed, 21 insertions(+), 15 deletions(-)
diff --git a/Assignment 1/assignment1.py b/Assignment 1/assignment1.py
index ec014de..7938956 100644
--- a/Assignment 1/assignment1.py
+++ b/Assignment 1/assignment1.py
@@ -8,9 +8,12 @@ b = np.transpose(b) #make b a column vector
D = np.asmatrix(np.ones(np.size(b)))
m = 0
# Make a guess for x vector
-x = np.asmatrix(np.zeros(np.size(b)))
-x = np.transpose(x) #make column vector
-alpha0 = 10
+#x = np.asmatrix(np.zeros(np.size(b)))
+#x = np.transpose(x) #make column vector
+#x=np.matrix(np.random.rand(5,1))
+x = np.transpose(np.asmatrix(np.ones(np.size(b)))*0.1)
+
+alpha0 = 1000.0
count = 0
# Define f(x)
def f(Q,b,c,x):
@@ -24,11 +27,11 @@ def gradf(Q,b,x):
def armijo(alpha0,Q,b,c,D,m):
alpha = alpha0
- print('alpha is ', alpha)
- s = 1
- sigma = 10e-1
+ #print('alpha is ', alpha)
+ s = 1.0
+ sigma = 1.0
beta = 1.0/2
- while f(Q,b,c,x+np.transpose(alpha*D)) > f(Q,b,c,x) + sigma*alpha*(np.transpose(gradf(Q,b,x)))*np.transpose(D):
+ while f(Q,b,c,x+np.transpose(beta**m*alpha*D)) > f(Q,b,c,x) + sigma*beta**m*alpha*(np.transpose(gradf(Q,b,x)))*np.transpose(D):
m+=1
#print('m is ', m)
alpha = beta**m*s
@@ -45,15 +48,18 @@ def countval():
return count
# Begin Gradient Descent Algorithm
-def grad_opt(epsilon,x,count):
- alpha = armijo(alpha0,Q,b,c,D,m)
- xnew = x
+def grad_opt(epsilon,x,count,alpha):
#print('alpha is ', alpha)
while np.linalg.norm(gradf(Q,b,x))>= epsilon:
+ alpha = armijo(alpha,Q,b,c,D,m)
+ #print('alpha0 is ', alpha)
count += 1
- #print('f(x) is ', f(Q,b,c,x))
- print('norm of gradf(x) is ', np.linalg.norm(gradf(Q,b,x)))
- xnew -= alpha*gradf(Q,b,x)
+ if count%1000==0:
+ print('f(x) is ', f(Q,b,c,x))
+
+ #print('norm of gradf(x) is ', np.linalg.norm(gradf(Q,b,x)))
+ x -= alpha*gradf(Q,b,x)
+ alpha = alpha0
print('Done')
print('x* is ', x)
@@ -65,10 +71,10 @@ def grad_opt(epsilon,x,count):
def run(epsilon):
xstart = xval()
countstart = countval()
- grad_opt(epsilon,xstart,countstart)
+ grad_opt(epsilon,xstart,countstart,alpha0)
return 0
-run(0.8895)
+run(0.889)
--
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