Operator Splitting Methods for Convex and Nonconvex Optimization

This dissertation focuses on a family of optimization methods called operator splitting methods. They solve complicated problems by decomposing the problem structure into simpler pieces and make progress on each of them separately. Over the past two decades, there has been a resurgence of interests in these methods as the demand for solving structured large-scale problems grew. One of the major challenges for splitting methods is their sensitivity to ill-conditioning, which often makes them struggle to achieve a high order of accuracy. Furthermore, their classical analyses are restricted to the nice settings where solutions do exist, and everything is convex. Much less is known when either of these assumptions breaks down.This work aims to address the issues above. Specifically, we propose a novel acceleration technique called inexact preconditioning, which exploits second-order information at relatively low computation cost. We also show that certain splitting methods still work on problems without solutions, in the sense that their iterates provide information on what goes wrong and how to fix. Finally, for nonconvex problems with saddle points, we show that almost surely, splitting methods will only converge to the local minimums under certain assumptions

Propagating functional dependencies with conditions

The dependency propagation problem is to determine, given a view defined on data sources and a set of dependencies on the sources, whether another dependency is guaranteed to hold on the view. This paper investigates dependency propagation for recently proposed conditional functional dependencies (CFDs). The need for this study is evident in data integration, exchange and cleaning since dependencies on data sources often only hold conditionally on the view. We investigate dependency propagation for views defined in various fragments of relational algebra, CFDs as view dependencies, and for source dependencies given as either CFDs or traditional functional dependencies (FDs). (a) We establish lower and upper bounds, all matching , ranging from PTIME to undecidable. These not only provide the first results for CFD propagation, but also extend the classical work of FD propagation by giving new complexity bounds in the presence of finite domains. (b) We provide the first algorithm for computing a minimal cover of all CFDs propagated via SPC views; the algorithm has the same complexity as one of the most efficient algorithms for computing a cover of FDs propagated via a projection view, despite the increased expressive power of CFDs and SPC views. (c) We experimentally verify that the algorithm is efficient. </jats:p

Design Method of Bending Load-Carrying Capacity for Sandwich Panels with Different Metal Panel on Both Sides

The sandwich panels, with plain and shallow grain pressed metal plate as the face sheets, and glass wools, rigid polyurethane foam, and rock wools as core materials, have excellent heat insulation and mechanical behavior, and been used as curtain walls for tall buildings in recent years in China. Since wind load and temperature action are the main actions for curtain walls, the sandwich panels are flexural members. In this paper, the design method and design formula of flexural load-carrying capacity and flexural deflection of a kind of sandwich plates with different metal panel on both sides are discussed and proposed. This proposed method considers the different load types, like uniform load, concentrated load, and temperature action, and different core materials. The FE Method can be verified by comparing on shear force distribution coefficients for different sandwich panels with same metal panels on both sides between FE results and calculated results. Then the FE Method can be used to verify the proposed method for shear force distribution coefficients of sandwich plates with different metal panel on both sides. Finally, the proposed method for bending load-carrying capacities for sandwich plates with different metal panel on both sides is verified using FE Method. These verifies show that the proposed method for shear force distribution coefficients and bending load-carrying capacities for sandwich plates with different metal panel on both sides is safe and suitable