On the singular hyperbolicity of star flows

We prove for a generic star vector field $X$ that, if for every chain recurrent class $C$ of $X$ all singularities in $C$ have the same index, then the chain recurrent set of $X$ is singular hyperbolic. We also prove that every Lyapunov stable chain recurrent class of $X$ is singular hyperbolic. As a corollary, we prove that the chain recurrent set of a generic 4-dimensional star flow is singular hyperbolic.Comment: 29 pages, version to appear in J. Mod. Dy

A unified variance-reduced accelerated gradient method for convex optimization

We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition number, Varag exhibits the unified optimal rates of convergence for solving smooth convex finite-sum problems directly regardless of their strong convexity. Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence. It also establishes an optimal linear rate of convergence for solving a wide class of problems only satisfying a certain error bound condition rather than strong convexity. Varag can also be extended to solve stochastic finite-sum problems.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019

The Expansion of Chinese Construction Companies in the Global Market

Chinese contractors are increasingly playing a significant role in the global construction market. This thesis provides a comprehensive study of the global expansion of Chinese construction companies as a result of Chinese open-door policies, by describing their developments from 1950 to 2008, highlighting their achievements, and identifying the main constraints preventing them from playing a more effective and efficient role in the global construction market. The development of Chinese construction companies in the global market was divided into three periods: the first period from 1950 to 1978, the second period from 1979 to 2001, and the third period from 2002 to 2008. In each period, the autonomy of Chinese construction companies, along with their achievements and problems were studied. Besides, the new business environment after accession to the World Trade Organization (WTO) and the analyses on Chinese foreign economic cooperation and on the top Chinese contractors (Top CC) using the data since 1979 were conducted. The results of this thesis can help the U.S. construction companies become more familiar with the Chinese construction companies and therefore more competitive in the global construction market