  Intelligent reflecting surfaces (IRSs) are revolutionary enablers for
next-generation wireless communication networks, with the ability to customize
the radio propagation environment. To fully exploit the potential of
IRS-assisted wireless systems, reflective elements have to be jointly optimized
with conventional communication techniques. However, the resulting optimization
problems pose significant algorithmic challenges, mainly due to the large-scale
non-convex constraints induced by the passive hardware implementations. In this
paper, we propose a low-complexity algorithmic framework incorporating
alternating optimization and gradient-based methods for large-scale
IRS-assisted wireless systems. The proposed algorithm provably converges to a
stationary point of the optimization problem. Extensive simulation results
demonstrate that the proposed framework provides significant speedups compared
with existing algorithms, while achieving a comparable or better performance.
