In this work we propose solving huge-scale instances of the truss
topology design problem with coordinate descent methods.
We develop four efficient codes: serial and parallel
implementations of randomized and greedy rules for the
selection of the variable (potential bar) to be updated in the next
iteration. Both serial methods enjoy an 
iteration complexity
guarantee, where 
is the number of potential bars and 
the
iteration counter. Our parallel implementations, written in CUDA and
running on a graphical processing unit (GPU), are capable of speedups of
up to two orders of magnitude when compared to their serial counterparts.
Numerical experiments were performed on instances with up to 30 million
potential bars.