An example in which CRCQ holds. The left figure shows a set S(u) defined by 3 constraints. The normal cone NS(u)(x) is the cone generated by the two dashed halflines originated from the point x. The red curve indicates the neighborhood X. The normal cone NS(u)(x) has four nonempty faces, and the family {I(x′, u), x′ ∈ S(u)∩X} contains four elements {1, 3},{1},{3} and ∅, each of which correspond...

Abstrac t In most approaches to device simulation a set of coupled paitial differential equations must be solved. The solution is mainly determined by the applied boundary conditions. This paper critically investigates the commonly used types of boundary conditions from both the mathematical and the numerical points of view. Consistency and convergence behavior are illustrated with computationa...

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...

We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuousand discrete-time. It has been shown in [27] that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices and we show t...

We consider fully nonlinear parabolic equations on bounded domains under Dirichlet boundary condition. Assuming that the equation and the domain satisfy certain symmetry conditions, we prove that each bounded positive solution of the Dirichlet problem is asymptotically symmetric. Compared with previous results of this type, we do not assume certain crucial hypotheses, such as uniform (with resp...

In this work we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multidimensional or cyclic filter banks as well as filter banks for signals in `(Z×Zs) or `(Zr ×Zs) spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds.

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...

In this paper, a model of an optimal control problem with chance constraints is introduced. The parametersof the constraints are fuzzy, random or fuzzy random variables. Todefuzzify the constraints, we consider possibility levels.  Bychance-constrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical op...

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 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,...