A modified method to identification of Lagrange multipliers

On the Method of Lagrange Multipliers

and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...

Canonical approach to Lagrange multipliers

Lagrange multipliers are present in any gauge theory. They possess peculiar gauge transformation which is not generated by the constraints in the model as it is the case with the other variables. For rank one gauge theories we show how to alter the constraints so that they become generators of the local symmetry algebra in the space of Lagrange multipliers too. We also discuss the limitations o...

A Variational Approach to Lagrange Multipliers

We discuss Lagrange multiplier rules from a variational perspective. This allows us to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.

Substructuring by Lagrange Multipliers

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...