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UID:submissions.pasc-conference.org_PASC24_sess153_msa169@linklings.com
SUMMARY:Adaptive Randomized Sketching for Dynamic Nonsmooth Optimization
DESCRIPTION:Minisymposium\n\nRobert Baraldi and Drew Kouri (Sandia Nationa
 l Laboratories) and Harbir Antil (George Mason University)\n\nDynamic opti
 mization problems arise in many applications, such as optimal flow control
 , full waveform inversion, and medical imaging. Despite their ubiquity, su
 ch problems are plagued by significant computational challenges. For examp
 le, memory is often a limiting factor when determining if a problem is tra
 ctable, since the evaluation of derivatives requires the entire state traj
 ectory.  Many applications additionally employ nonsmooth regularizers such
  as the L1-norm or the total variation, as well as auxiliary constraints o
 n the optimization variables. We introduce a novel trust-region algorithm 
 for minimizing the sum of a smooth, nonconvex function and a nonsmooth, co
 nvex function that addresses these two challenges. Our algorithm employs r
 andomized 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 t
 he efficacy of our method on a few control problems in dynamic PDE-constra
 ined optimization.\n\nDomain: Climate, Weather, and Earth Sciences, Engine
 ering, Life Sciences, Computational Methods and Applied Mathematics\n\nSes
 sion Chair: Robert Baraldi (Sandia National Laboratories)
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