In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose a given tensor block into blocks of smaller size, where the size is characterized by a set of mode-n ranks. We study different types of such decompositions. For each type we derive conditions under which essential uniqueness is guaranteed. The parallel factor decomposition and Tucker’s decomposition can b...

This paper is concerned with the problem of finding a Tucker decomposition for tensors. Traditionally, solution methods for Tucker decomposition presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in some applications. In this paper we propose a new computational model where the configuration and the size of the core become a part of the dec...

The Kuhn-Tucker model of Wales and Woodland (1983) provides a utility theoretic framework for estimating preferences over commodities for which individuals choose not to consume one or more of the goods. Due to the complexity of the model, however, there have been few applications in the literature and little attention has been paid to the problems of welfare analysis within the Kuhn-Tucker fra...

The aim of the chapter is to introduce a new technology using the flow-divided electrodes for sewage reclamation based on redox and concentrating ions. This creative system can be used directly for sewage treatment without the need for costly ion-exchange membranes and other chemical reagents. Under experimental condi‐ tions, the removal percentage of TDS (total dissolved salts) is 83 %and the ...

Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems...

This paper shows the relationship between degeneracy degrees and multiplicities in linear programming models. The usual definition of degeneracy is restricted to vertices of a polyhedron. We introduce degeneracy for nonempty subsets of polyhedra and show that for linear programming models for which the feasible region contains at least one vertex holds that the dimension of the optimal face is ...

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...