Abstract. We consider Tucker-like approximations with an r × r × r core tensor for threedimensional n×n×n arrays in the case of r ¿ n and possibly very large n (up to 104−106). As the approximation contains only O(rn + r3) parameters, it is natural to ask if it can be computed using only a small amount of entries of the given array. A similar question for matrices (two-dimensional tensors) was ...

The Consecutive-Ones Property (C1P) in binary matrices is a combinatorial concept with applications in several area, from graph planarity testing to computational biology. Tucker patterns are families of submatrices that characterize non-C1P matrices, and thus represent natural certificates of non-C1P matrices. However, there are very few algorithmic results regarding Tucker patterns. In the pr...

This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn–Tucker) conditions for optimality ...

In this paper we give necessary optimality conditions of Fritz-John and Kuhn-Tucker (KKT) conditions for non-linear infinite dimensional programming problem with operatorial constraints. We use an alternative theorem. Some of the known results in finite dimensional case have been extended to infinite dimensional case with suitable conditions.

⎯ The aim of the present work is to characterize weakly efficient solution of multiobjective programming problems under the assumptions of α-invexity, using the concepts of critical point and Kuhn-Tucker stationary point for multiobjective programming problems. In this paper, we also extend the above results to the nondifferentiable multiobjective programming problems. The use of α-invex functi...

This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear 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 relat...

This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave 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 to the Kuhn...

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...