Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers

REGULARITY OF LAGRANGE MULTIPLIERS FOR OPTIMAL CONTROL PROBLEMS WITH PDEs AND MIXED CONTROL STATE CONSTRAINTS

Lagrange multipliers for distributed parameter systems with mixed control-state constraints may exhibit better regularity properties than those for problems with pure pointwise state constraints, (1), (2), (4). Under natural assumptions, they are functions of certain L-spaces, while Lagrange multpliers for pointwise state constraints are, in general, measures. Following an approach suggested in...

Efficient Preconditioners Based on Fictitious Domains for Elliptic Fe{problems with Lagrange Multipliers Eecient Preconditioners Based on Ctitious Domains for Elliptic Fe{problems with Lagrange Multipliers

The macro{hybrid formulation based on domain decomposition is considered for elliptic boundary value problems with both symmetric positive deenite and indeenite operators. The problem is discretized by the mortar element method, which leads to a large{scale sparse linear system with a saddle{ point matrix. In the case of symmetric and positive deenite operators, a block diagonal preconditioner ...

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...

Domain Decomposition with 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...