In this paper we study the sedimentation of several thousand circular particles in 2D using the method of distributed Lagrange multipliers for solid-liquid ow. The simulation gives rise to ngering which resembles Rayleigh-Taylor instabilities. The waves have a well de ned wavelength and growth rate which can be modeled as a conventional Rayleigh-Taylor instability of heavy uid above light. The ...

Manyeconomicmodels andoptimizationproblemsgenerate (endogenous) shadow prices—alias dual variables or Lagrange multipliers. Frequently the “slopes” of resulting price curves—that is, multiplier derivatives—are of great interest. These objects relate to the Jacobian of the optimality conditions. That particular matrix often has block structure. So, we derive explicit formulas for the inverse of ...

We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lamé equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrang...

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether’s theorem to fractional optima...

A quadratic programming problem with positive definite Hessian and bound constraints is solved, using a Lagrange multiplier approach. The proposed method falls in the category of exterior point, active set techniques. An iteration of our algorithm modifies both the minimization parameters in the primal space and the Lagrange multipliers in the dual space. Comparative results of numerical experi...

2 Methods 2 2.1 Lagrange Multiplier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Pegging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Interior-Point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.2 Interior-Point Algorithm ....