In this work we deal with thick brane solutions in the warped five-dimensional braneworld scenario a single extra spatial dimension of infinite extent, for class modified theories gravity Lagrange multiplier. We first present action, describe and field equations, outline strategy to find explicit explore stability gravitational sector. The investigation deals mainly construction order framework...

In this work we present new weak conditions that ensure the validity of necessary second order optimality conditions (SOC) for nonlinear optimization. We are able to prove that weak and strong SOCs hold for all Lagrange multipliers using Abadie-type assumptions. We also prove weak and strong SOCs for at least one Lagrange multiplier imposing the Mangasarian-Fromovitz constraint qualification an...

This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker ...

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivative...