Symes, William W.2012-07-032012-07-032010-122011Enriquez, Marco. "The Effects of Coupling Adaptive Time-Stepping and Adjoint-State Methods for Optimal Control Problems." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/64429">https://hdl.handle.net/1911/64429</a>.https://hdl.handle.net/1911/64429This thesis presents the implications of using adaptive time-stepping schemes with the adjoint-state method, a widely used algorithm for computing derivatives in optimal-control problems. Though we gain control over the accuracy of the timestepping scheme, the forward and adjoint time grids become mismatched. Despite this fact, I claim using adaptive time-stepping for optimal control problems is advantageous for two reasons. First, taking variable time-steps potentially reduces the computational cost and improves accuracy of the forward and adjoint equations' numerical solution. Second, by appropriately adjusting the tolerances of the timestepping scheme, convergence of the optimal control problem can be theoretically guaranteed via inexact Newton theory. I present proofs and computational results to support this claim.131 ppapplication/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.Applied MathematicsThesisEnriquezM