  We consider the problem of minimizing the sum of three functions, one of
which is nonconvex but differentiable, and the other two are convex but
possibly nondifferentiable. We investigate the Three Operator Splitting method
(TOS) of Davis & Yin (2017) with an aim to extend its theoretical guarantees
for this nonconvex problem template. In particular, we prove convergence of TOS
with nonasymptotic bounds on its nonstationarity and infeasibility errors. In
contrast with the existing work on nonconvex TOS, our guarantees do not require
additional smoothness assumptions on the terms comprising the objective; hence
they cover instances of particular interest where the nondifferentiable terms
are indicator functions. We also extend our results to a stochastic setting
where we have access only to an unbiased estimator of the gradient. Finally, we
illustrate the effectiveness of the proposed method through numerical
experiments on quadratic assignment problems.
