Knowledge graphs have been demonstrated to be an effective tool for numerous intelligent applications. However, a large amount of valuable knowledge still exists implicitly in the graphs. To enrich existing graphs, recent years witnessed that many algorithms link prediction and embedding designed infer new facts. But most these studies focus on static ignore temporal information which reflects ...

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications introduce a weak qualification which assures the equivalence between SCAKKT Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483-500, 1994) problems.

A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...

The tensor-structured methods developed recently for the accurate calculation of the Hartree and the non-local exchange operators have been applied successfully to the ab initio numerical solution of the Hartree-Fock equation for some molecules. In the present work, we show that the rank-structured representation can be gainfully applied to the accurate approximation of the electron density of ...

Analysis of high dimensional data in modern applications, such as neuroscience, text mining, spectral analysis or chemometrices naturally requires tensor decomposition methods. The Tucker decompositions allow us to extract hidden factors (component matrices) with a different dimension in each mode and investigate interactions among various modes. The Alternating Least Squares (ALS) algorithms h...

The Kuhn-Tucker and envelope theorems can be used to characterize the solution to a wide range of constrained optimization problems: static or dynamic, under perfect foresight or featuring randomness and uncertainty. In addition, these same two results provide foundations for the work on the maximum principle and dynamic programming that we will do later on. For both of these reasons, the Kuhn-...

Analyses of array-valued datasets often involve reduced-rank array approximations, typically obtained via least-squares or truncations of array decompositions. However, least-squares approximations tend to be noisy in high-dimensional settings, and may not be appropriate for arrays that include discrete or ordinal measurements. This article develops methodology to obtain low-rank model-based re...

Gated networks are that contain gating connections in which the output of at least two neurons multiplied. The basic idea a gated restricted Boltzmann machine (RBM) model is to use binary hidden units learn conditional distribution one image (the output) given another input). This allows RBM transformations between successive images. Inference consists extracting pair However, fully connected m...

This paper presents a constrained Tucker-3 model for blind beamforming. The constrained structure of this model is parameterized by two constraint matrices that capture the spatial and temporal structure of the channel. We first present a generalized Tucker-3 model that considers a multipath propagation scenario with large delay spread and different number of paths per source. This tensor model...