In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

A new class of weak weighted derivatives and its associated Sobolev spaces is introduced and studied. The proposed notion uses a variational formulation in its definition which generalizes the usual weighting of the classical weak derivative. Such a construction naturally leads to Sobolev spaces containing classes of discontinuous functions. Weak closedness with respect to both varying function...

For a lattice system with a finite number of Fermions and spins on each lattice point, conditional expectations relative to an even product state (such as Fermion Fock vacuum) are introduced and the corresponding standard potential for any given dynamics, or more generally for any given time derivative (at time 0) of strictly local operators, is defined, with the case of the tracial state previ...

We use Chen iterated line integrals to construct a topological algebra Ap of separating functions on the Group of Loops LMp. Ap has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops L̃Mp. Then we develope a Loop Calculus, based on the Endpoint and Area Derivative Operators, providing a rigo...

This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body tha...

We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path o...

We consider structure preserving numerical schemes for the Ostrovsky equation, which describes gravity waves under the influence of Coriolis force. This equation has two associated invariants: an energy function and the L norm. It is widely accepted that structure preserving methods such as invariants-preserving and multi-symplectic integrators generally yield qualitatively better numerical res...

Abstract In this study, the modified fractal gas dynamics model (GDM) with variable coefficients is successfully represented using derivative. We obtain variational principle of GDM by employing semi‐inverse method. Based on established principle, a new and fascinating algorithm presented to solve model, which called two‐scale method (FTSVM). Finally, two numerical examples are given indicate e...

The classical solution and the strong of a partial differential equation problem are continuously differentiable solutions. This has derivative for continuous infinity level. However, not all problems equations can be easily obtained by Even existence requires in-depth investigation. variational formulation method qualitatively analyze single to problem. study provides an alternative in analyzi...

Abstract From the socio-epistemology perspective, teaching of derivative is problematized due to lack reference frameworks that give variational meanings and allow its construction by means graphical arguments. The objective this research was analyze derivative, as a rate change, Chilean students developed through graphic argumentation in specific situation variation. In order respond stated ob...