Curved, linear Kirchhoff beams formulated using tangential differential calculus and Lagrange multipliers

Continuous/discontinuous finite element modelling of Kirchhoff plate structures in R3 using tangential differential calculus

We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using C0-elements for the...

Lagrange Multipliers and Optimality

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

The Linear Nonconvex Generalized Gradient and Lagrange Multipliers

A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...

Substructuring by Lagrange Multipliers

Optional decomposition and Lagrange multipliers

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand φ such that the difference X−φ ·S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rat...