Nash, StephenEmelianenko, MariaDi, Zichao2013-08-192013-08-192013-08https://hdl.handle.net/1920/8363In this thesis, we apply the multilevel optimization framework (MG/OPT) to a class of vector quantization problem. Specially, we focus on a problem called centroidal Voronoi tessellations (CVTs). MG/OPT is a generalization of traditional multigrid for solving partial differential equations. This framework assumes that there exists a hierarchy of models of the underlying optimization problem, corresponding to levels of detail in the problem, and the interest is to find the solution at the nest level. The intent of MG/OPT is to use calculations on ate the progress of the optimization on the nest level.114 pagesenCopyright 2013 Zichao DiApplied mathematicsMultigridNonlinear programmingOptimal controlOptimizationVector quantizationDissertation