Alternating Minimization Methods for Solving Multilinear Systems

Recent works on the multilinear system A x m − 1 = b with an order- m and dimension- n tensor A and a vector b of dimension- n have been motivated by their applications in data mining, numerical PDEs, tensor complementary problems, and so on. In this paper, we propose an alternating minimization method for the solution of the system mentioned above and present several randomized versions of this algorithm in order to improve its performance. The provided numerical experiments show that our methods are feasible for any tensor A and outperform some existing ones in the same case.

Some results on the filter method for nonlinear complementary problems

Recent studies show that the filter method has good numerical performance for nonlinear complementary problems (NCPs). Their approach is to reformulate an NCP as a constrained optimization solved by filter algorithms. However, they can only prove that the iterative sequence converges to the KKT point of the constrained optimization. In this paper, we investigate the relation between the KKT point of the constrained optimization and the solution of the NCP. First, we give several sufficient conditions under which the KKT point of the constrained optimization is the solution of the NCP; second, we define regular conditions and regular point which include and generalize the previous results; third, we prove that the level sets of the objective function of the constrained optimization are bounded for a strongly monotone function or a uniform P-function; finally, we present some examples to verify the previous results.

NLP-driven citation analysis for scientometrics

This paper summarizes ongoing research in Natural-Language-Processing-driven citation analysis and describes experiments and motivating examples of how this work can be used to enhance traditional scientometrics analysis that is based on simply treating citations as a ‘vote’ from the citing paper to cited paper. In particular, we describe our dataset for citation polarity and citation purpose, present experimental results on the automatic detection of these indicators, and demonstrate the use of such annotations for studying research dynamics and scientific summarization. We also look at two complementary problems that show up in Natural-Language-Processing-driven citation analysis for a specific target paper. The first problem is extracting citation context, the implicit citation sentences that do not contain explicit anchors to the target paper. The second problem is extracting reference scope, the target relevant segment of a complicated citing sentence that cites multiple papers. We show how these tasks can be helpful in improving sentiment analysis and citation-based summarization.

A Smooth System of Equations Approach to Complementarity Problems for Frictionless Contacts

Frictionless contact problems are the simplest and classical contact problems, and the contact conditions of sticking, slipping, and separation mode all can be ascribed to complementary problems. Consequently, a smooth system of equations approach for the design and analysis of complementarity problems for frictionless contacts is presented. A compute program based on boundary element technique is given and applied to two practical contact examples. The validity and accuracy of the proposed method are demonstrated.