A matrix always has a full rank submatrix such that the of this is equal to submatrix. This property one corner stones theory. We call max-full-rank-submatrix property. Tensor ranks play crucial role in low tensor approximation, completion and recovery. However, their theory still not matured yet. Can we set an axiom system for ranks? extend tensors? explore these paper. first propose some axio...

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.

This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker Saddle and Stationary points are characterized. In addition, some important theorems related...

In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. The constraint set being defined by C = g−1(K) where g is a smooth map between Banach spaces, and K a closed convex cone, we show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to metric subregularity of the multifunction defining the constraint, and...

The Kuhn-Tucker model provides a utility theoretic framework for estimating preferences over commodities for which individuals choose not to consume one or more of the goods. This paper provides an application of the Kuhn-Tucker model to the problem of recreation demand and site selection, modeling the demand for fishing in the Wisconsin Great Lakes region. Disciplines Agricultural and Resource...

Some theoretical difficulties that arise from dimensionality reduction for tensors with non-negative coefficients is discussed in this paper. A necessary and sufficient condition is derived for a low nonnegative rank tensor to admit a non-negative Tucker decomposition with a core of the same non-negative rank. Moreover, we provide evidence that the only algorithm operating mode-wise, minimizing...

Abstract Knowledge Graph Embedding (KGE) translates entities and relations of knowledge graphs (KGs) into a low-dimensional vector space, enabling an efficient way predicting missing facts. Generally, KGE models are trained with positive negative examples, discriminating positives against negatives. Nevertheless, KGs contain only facts; training requires generating negatives from non-observed o...