Minisymposium Presentation

Dynamic optimization problems arise in many applications, such as optimal flow control, full waveform inversion, and medical imaging. Despite their ubiquity, such problems are plagued by significant computational challenges. For example, memory is often a limiting factor when determining if a problem is tractable, since the evaluation of derivatives requires the entire state trajectory. Many applications additionally employ nonsmooth regularizers such as the L1-norm or the total variation, as well as auxiliary constraints on the optimization variables. We introduce a novel trust-region algorithm for minimizing the sum of a smooth, nonconvex function and a nonsmooth, convex function that addresses these two challenges. Our algorithm employs randomized sketching to store a compressed version of the state trajectory for use in derivative computations. By allowing the trust-region algorithm to adaptively learn the rank of the state sketch, we arrive at a provably convergent method with near optimal memory requirements. We demonstrate the efficacy of our method on a few control problems in dynamic PDE-constrained optimization.