Elastic Damping Mechanism Optimization by Indefinite Lagrange Multipliers

Substructuring by Lagrange Multipliers

Inextensible elastic rods with torsional friction based on Lagrange multipliers

Elastic rods are thin flexible objects typically undergoing large non-linear deformations that cannot be modeled with linear methods. They are used in a number of research fields, e. g., to represent hair or ropes in animations, or catheters or needles in medical simulations. In this paper, we propose a deformation model for inextensible elastic rods. The method of Lagrange multipliers is emplo...

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 Theory of Discrete Lagrange Multipliers for Nonlinear Discrete Optimization

In this paper we present a Lagrange-multiplier formulation of discrete constrained optimization problems, the associated discrete-space first-order necessary and sufficient conditions for saddle points, and an efficient first-order search procedure that looks for saddle points in discrete space. Our new theory provides a strong mathematical foundation for solving general nonlinear discrete opti...

Lagrange Multipliers with Optimal Sensitivity Properties in Constrained Optimization

We consider optimization problems with inequality and abstract set constraints, and we derive sensitivity properties of Lagrange multipliers under very weak conditions. In particular, we do not assume uniqueness of a Lagrange multiplier or continuity of the perturbation function. We show that the Lagrange multiplier of minimum norm defines the optimal rate of improvement of the cost per unit co...