Difference between GradientDescentOptimizer and AdamOptimizer in tensorflow?

When using GradientDescentOptimizer instead of Adam Optimizer the model doesn't seem to converge. On the otherhand, AdamOptimizer seems to work fine. Is the something wrong with the GradientDescentOptimizer from tensorflow?

import matplotlib.pyplot as plt
import tensorflow as tf
import numpy as np

def randomSample(size=100):
    """
    y = 2 * x -3
    """
    x = np.random.randint(500, size=size)
    y = x * 2  - 3 - np.random.randint(-20, 20, size=size)    

    return x, y

def plotAll(_x, _y, w, b):
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(_x, _y)

    x = np.random.randint(500, size=20)
    y = w * x + b
    ax.plot(x, y,'r')
    plt.show()

def lr(_x, _y):

    w = tf.Variable(2, dtype=tf.float32)
    b = tf.Variable(3, dtype=tf.float32)

    x = tf.placeholder(tf.float32)
    y = tf.placeholder(tf.float32)

    linear_model = w * x + b
    loss = tf.reduce_sum(tf.square(linear_model - y))
    optimizer = tf.train.AdamOptimizer(0.0003) #GradientDescentOptimizer
    train = optimizer.minimize(loss)

    init = tf.global_variables_initializer()
    sess = tf.Session()
    sess.run(init)
    for i in range(10000):
        sess.run(train, {x : _x, y: _y})
    cw, cb, closs = sess.run([w, b, loss], {x:_x, y:_y})
    print(closs)
    print(cw,cb)

    return cw, cb

x,y = randomSample()
w,b = lr(x,y)
plotAll(x,y, w, b)