Asynchronous Distributed ADMM for Large-Scale Optimization- Part II: Linear Convergence Analysis and Numerical Performance

The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the AD-ADMM on a high-performance computer cluster by solving a large-scale logistic regression problem.Comment: submitted for publication, 28 page

An Empirical Note on Testing the Cointegration Relationship Between the Real Estate and Stock Markets in Taiwan

This note studies the long-run relationship between real estate and stock markets in the Taiwan context over the 1986Q3 to 2006Q4 period, using standard cointegration test of Johansen and Juselius (1990) and that of Engle-Granger (1987) as well as the fractional cointegration test of Geweke and Porter-Hudak (1983). The results from both types of cointegration tests strongly indicate that these two markets are not cointegrated with each other. With respect to risk diversification, it is obvious that investors and financial institutions should have included both assets in the same portfolio during that period.