  Training deep neural networks (DNNs) efficiently is a challenge due to the
associated highly nonconvex optimization. The backpropagation (backprop)
algorithm has long been the most widely used algorithm for gradient computation
of parameters of DNNs and is used along with gradient descent-type algorithms
for this optimization task. Recent work have shown the efficiency of block
coordinate descent (BCD) type methods empirically for training DNNs. In view of
this, we propose a novel algorithm based on the BCD method for training DNNs
and provide its global convergence results built upon the powerful framework of
the Kurdyka-Lojasiewicz (KL) property. Numerical experiments on standard
datasets demonstrate its competitive efficiency against standard optimizers
with backprop.
