  We propose a general alternating minimization algorithm for nonconvex
optimization problems with separable structure and nonconvex coupling between
blocks of variables. To fix our ideas, we apply the methodology to the problem
of blind ptychographic imaging. Compared to other schemes in the literature,
our approach differs in two ways: (i) it is posed within a clear mathematical
framework with practically verifiable assumptions, and (ii) under the given
assumptions, it is provably convergent to critical points. A numerical
comparison of our proposed algorithm with the current state-of-the-art on
simulated and experimental data validates our approach and points toward
directions for further improvement.
