In this paper we study uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. The main tool in our investigation of this question will be a calculus of dual (polar) cones. We give sufficient and in some cases necessary conditions for uniqueness of Lagrange multipliers in general Banach spaces. General results are then applied to two particular examples of the s...

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressur...

A rule to assign physical meaning to Lagrange multipliers is discussed. Examples from mechanics, statistical mechanics and quantum mechanics are given.

A new flexibility-based component mode synthesis method is presented, which is derived by approximating the partitioned equations of motion that employ a localized method of Lagrange multipliers. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without any redundancies at multiply connected interfac...

We study homological invariants of smooth families of real quadratic forms as a step towards a “ Lagrange multipliers rule in the large” that intends to describe topology of smooth vector functions in terms of scalar Lagrange functions.

Recently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the output and input probability density function (pdf) of the deconvolutional process were approximated with the maximum entropy density approximation tech...

It is known that when the set of Lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton, this set may contain so-called critical multipliers. This special subset of Lagrange multipliers defines, to a great extent, stability pattern of the solution in question subject to parametric perturbations. Criticality of a Lagrange multiplier can b...

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multiplie...