Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers

Bilinear Factorization via Augmented Lagrange Multipliers

This paper presents a unified approach to solve different bilinear factorization problems in Computer Vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization problem where one of the factors is constrained to lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem. Thi...

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...

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...