The term for cost / weight decay is not part of the optimizers in TensorFlow.
It is easy to include, however, adding an additional penalty to the cost function with the loss of L2 on the scales:
C = <your initial cost function> l2_loss = tf.add_n([tf.nn.l2_loss(v) for v in tf.trainable_variables()]) C = C + lambda * l2_loss
tf.nn.l2_loss(v) link is just 0.5 * tf.reduce_sum(v * v) , and the gradients for the individual weights will be lambda * w , which should be equivalent to your bound equation.
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