Heinkenschloss, Matthias2024-01-222024-01-222024-052023-12-12May 2024Kroeger, Nathaniel James. "ADMM and Diagonalization Based Parallel-in-Time Methods for Optimal Control Problems." (2023) PhD diss., Rice University. https://hdl.handle.net/1911/115344https://hdl.handle.net/1911/115344This thesis investigates alternating direction method of multipliers (ADMM) and diagonalization - based parallel-in-time methods for linear-quadratic partial differential equation (PDE)-constrained optimization problems. The solution of such optimization problems is computing time and memory intensive, and efficient methods are essential to making such problems computationally tractable. Two parallel-in-time approaches are considered. In the first approach, ADMM is applied to a time domain decomposition (TDD) formulation. ADMM tailored to the TDD formulation requires the parallel solution of smaller subdomain problems and reduces the number of variables that need to be kept in memory globally. Thus, ADMM carries out the parallelization-in-time because the ADMM subproblems are able to be broken down by time subdomain. In the second approach, a diagonalization technique is used to parallelize-in-time. This approach is then extended to handle inequality constraints. The inequality constraints extension is handled by a combination of diagonalization and ADMM - the ADMM algorithm is the “main” algorithm, while the diagonalization method handles the computationally expensive substep in ADMM. Here, the diagonalization provides the parallelism in time, while the ADMM algorithm decouples the inequality constraints from the rest of the optimal control problem. Numerical results are provided to show the effectiveness of these methods.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.PDE constrained optimizationParallel in timeADMMDiagonalizationThesis2024-01-22