Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities

This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as polynomial optimization by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization. We also prove that the assumption of nonsingularity in Nie's method can be weakened as the finiteness of singularities. Some numerical examples are given to illustrate the efficiency of our method.Comment: 23 page

Linking business analytics to decision making effectiveness: a path model analysis

While business analytics is being increasingly used to gain data-driven insights to support decision making, little research exists regarding the mechanism through which business analytics can be used to improve decision-making effectiveness (DME) at the organizational level. Drawing on the information processing view and contingency theory, this paper develops a research model linking business analytics to organizational DME. The research model is tested using structural equation modeling based on 740 responses collected from U.K. businesses. The key findings demonstrate that business analytics, through the mediation of a data-driven environment, positively influences information processing capability, which in turn has a positive effect on DME. The findings also demonstrate that the paths from business analytics to DME have no statistical differences between large and medium companies, but some differences between manufacturing and professional service industries. Our findings contribute to the business analytics literature by providing useful insights into business analytics applications and the facilitation of data-driven decision making. They also contribute to manager's knowledge and understanding by demonstrating how business analytics should be implemented to improve DM

On singular value distribution of large dimensional auto-covariance matrices

Let $(\varepsilon_j)_{j\geq 0}$ be a sequence of independent $p-$dimensional random vectors and $\tau\geq1$ a given integer. From a sample $\varepsilon_1,\cdots,\varepsilon_{T+\tau-1},\varepsilon_{T+\tau}$ of the sequence, the so-called lag $-\tau$ auto-covariance matrix is $C_{\tau}=T^{-1}\sum_{j=1}^T\varepsilon_{\tau+j}\varepsilon_{j}^t$. When the dimension $p$ is large compared to the sample size $T$, this paper establishes the limit of the singular value distribution of $C_\tau$ assuming that $p$ and $T$ grow to infinity proportionally and the sequence satisfies a Lindeberg condition on fourth order moments. Compared to existing asymptotic results on sample covariance matrices developed in random matrix theory, the case of an auto-covariance matrix is much more involved due to the fact that the summands are dependent and the matrix $C_\tau$ is not symmetric. Several new techniques are introduced for the derivation of the main theorem