We study the convergence of the finite element method with Lagrange multipliers for approximately solving the Dirichlet problem for a second-order elliptic equation in a plane domain with piecewise smooth boundary. Assuming mesh refinements around the corners, we construct families of boundary subspaces that are compatible with triangular Lagrange elements in the interior, and we carry out the ...

The reconstruction of dynamic magnetic resonance imaging (dMRI) from partially sampled k-space data has to deal with a trade-off between the spatial resolution and temporal resolution. In this paper, a low-rank and sparse decomposition model is introduced to resolve this issue, which is formulated as an inverse problem regularized by robust principal component analysis (RPCA). The inverse probl...

Subgradient methods are popular tools for nonsmooth, convex minimization , especially in the context of Lagrangean relaxation; their simplicity has been a main contribution to their success. As a consequence of the nonsmoothness, it is not straightforward to monitor the progress of a subgradient method in terms of the approximate fulllment of optimality conditions, since the subgradients used i...

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...

A robotic system can be viewed as a collection of lower-dimensional systems that are coupled via reaction forces (Lagrange multipliers) enforcing holonomic constraints. Inspired by this viewpoint, letter presents novel formulation for nonlinear control subject to coupling constraints virtual “coupling” inputs abstractly play the role Lagrange multipliers. The main contribution is process - mirr...

We consider a FETI-DP formulation for the Stokes problem on nonmatching grids in 2D. The FETI-DP method is a domain decomposition method that uses Lagrange multipliers to match the solutions continuously across the subdomain boundaries in the sense of dual-primal variables. We use the mortar matching condition as the continuity constraints for the FETI-DP formulation. Moreover, to satisfy the c...

We consider optimization problems with second order stochastic dominance constraints formulated as a relation of Lorenz curves. We characterize the relation in terms of rank dependent utility functions, which generalize Yaari’s utility functions. We develop optimality conditions and duality theory for problems with Lorenz dominance constraints. We prove that Lagrange multipliers associated with...

Abstract Many problems encountered in systems theory and system identification require the solution of polynomial optimization problems, which have a polynomial objective function and polynomial constraints. Applying the method of Lagrange multipliers yields a set of multivariate polynomial equations. Solving a set of multivariate polynomials is an old, yet very relevant problem. It is little k...

In this paper, we study a mean-variance portfolio selection problem that has a probabilistic benchmark constraint. This constraint changes the problem into a nonconvex one but could be solved via the method of Lagrange multipliers, whose existence is crucial in the solution.

We consider the coupling of compressible and nearly incompressible materials within the framework of mortar methods. Taking into account the locking effect, we use a suitable discretization for the nearly incompressible material and work with a standard conforming discretization elsewhere. The coupling of different discretization schemes in different subdomains are handled by flexible mortar te...