This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tu...

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem ...

For the approximation of time-dependent data tensors and of solutions to tensor differential equations by tensors of low Tucker rank, we study a computational approach that can be viewed as a continuous-time updating procedure. This approach works with the increments rather than the full tensor and avoids the computation of decompositions of large matrices. In this method, the derivative is pro...

The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible end-goal, the Karush-Kuhn-Tucker theorem, which is one of the main results of nonlinear programming. Of course, in the present lectures we have to limit ourselves most of the time to the Karush...

The purpose of this paper is to characterize the weak Pareto optimality for multiobjective pseudoconvex problem. In fact, it is a first order optimality characterization that generalize the Karush-Kuhn-Tucker condition. Moreover, this work is an extension of the single-objective case [6] to the multiobjective one with pseudoconvex continuous functions. Mathematics Subject Classification: 46N10,...

This paper deals with semi-infifinite programming multiple fuzzy-valued objective functions. Firstly, some types of effificient solutions are proposed and illustrated in examples. Then, necessary suffificient Karush-Kuhn-Tucker optimality conditions for functions established.

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...

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with peri...