Scalable Peaceman-Rachford Splitting Method with Proximal Terms

Along with developing of Peaceman-Rachford Splittling Method (PRSM), many batch algorithms based on it have been studied very deeply. But almost no algorithm focused on the performance of stochastic version of PRSM. In this paper, we propose a new stochastic algorithm based on PRSM, prove its convergence rate in ergodic sense, and test its performance on both artificial and real data. We show that our proposed algorithm, Stochastic Scalable PRSM (SS-PRSM), enjoys the $O(1/K)$ convergence rate, which is the same as those newest stochastic algorithms that based on ADMM but faster than general Stochastic ADMM (which is $O(1/\sqrt{K})$). Our algorithm also owns wide flexibility, outperforms many state-of-the-art stochastic algorithms coming from ADMM, and has low memory cost in large-scale splitting optimization problems

The Free Cash Flow and Corporate Returns

Mcpherson (2018) and Jose, Lancaster, Stevens (1996) have written papers to examine the relationship between liquidity management and firm profitability. The literature establishes that the cash conversion cycle has an implication for the profitability and liquidity of a firm. We extend the time period and analyze the free cash flow instead of cash conversion cycle. We provide evidence that firms with higher free cash flows have higher risk adjusted stock returns

An Effective Combination of Different Order N-grams

In this paper an approach is proposed to combine different order N-grams based on the discriminative estimation criterion, on which the parameters of n-gram can be optimized. To raise the power of modeling language information, we propose several schemes to combine conventional different order n-gram language model. We employ Newton Gradient method to estimate the assumption probabilities and then test the optimally selected language model. We conduct experiments on the platform of conversion from Chinese pinyin to Chinese character. The experimental results show that the memory capacity of language model can be remarkably lowered with hide loss of accuracy. 1

Statistical Inference of Constrained Stochastic Optimization via Sketched Sequential Quadratic Programming

We consider statistical inference of equality-constrained stochastic nonlinear optimization problems. We develop a fully online stochastic sequential quadratic programming (StoSQP) method to solve the problems, which can be regarded as applying Newton's method to the first-order optimality conditions (i.e., the KKT conditions). Motivated by recent designs of numerical second-order methods, we allow StoSQP to adaptively select any random stepsize $\bar{\alpha}_t$, as long as $\beta_t\leq \bar{\alpha}_t \leq \beta_t+\chi_t$, for some control sequences $\beta_t$ and $\chi_t=o(\beta_t)$. To reduce the dominant computational cost of second-order methods, we additionally allow StoSQP to inexactly solve quadratic programs via efficient randomized iterative solvers that utilize sketching techniques. Notably, we do not require the approximation error to diminish as iteration proceeds. For the developed method, we show that under mild assumptions (i) computationally, it can take at most $O(1/\epsilon^4)$ iterations (same as samples) to attain $\epsilon$-stationarity; (ii) statistically, its primal-dual sequence $1/\sqrt{\beta_t}\cdot (x_t - x^\star, \lambda_t - \lambda^\star)$ converges to a mean-zero Gaussian distribution with a nontrivial covariance matrix depending on the underlying sketching distribution. Additionally, we establish the almost-sure convergence rate of the iterate $(x_t, \lambda_t)$ along with the Berry-Esseen bound; the latter quantitatively measures the convergence rate of the distribution function. We analyze a plug-in limiting covariance matrix estimator, and demonstrate the performance of the method both on benchmark nonlinear problems in CUTEst test set and on linearly/nonlinearly constrained regression problems.Comment: 57 pages, 3 figures, 11 table

Land snails (Mollusca: Gastropoda) of India: status, threats and conservation strategies

Land snails form an important component in the forest ecosystem. In terms of number of species, the phylum Mollusca, to which land snails belong, is the largest phylum after Arthropoda. Mollusca provide unique ecosystem services including recycling of nutrients and they provide a prey base for small mammals, birds, snakes and other reptiles. However, land snails have the largest number of documented extinctions, compared to any other taxa. Till date 1,129 species of land snails are recorded from Indian territory. But only basic information is known about their taxonomy and little is known of their population biology, ecology and their conservation status. In this paper, we briefly review status, threats and conservation strategies of land snails of India