Increased convergence speed by modifying armijo's rule to include beta^m

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)