The FETI method is based on introducing Lagrange multipliers along interfaces between subdomain to enforce continuity of local solutions [4]. It has been demonstrated to be numerically scalable in the case of second-order problems, thanks to a built-in “coarse grid” projection [3]. For high-order problems, especially with plate or shell finite element models in structural analysis, a two-level ...

In this paper we introduce a modified penalty function (MPF) method for solving a problem which minimizes a nonlinear programming subject to inequality constraints. Basically, this method is a combination of the modified penalty methods and the Lagrangian methods. It treats inequality constraints with a modified penalty function and avoids the indifferentiability of max {x, 0}. This method alte...

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct numerical simulation of rigid particulate flows in a Newtonian fluid was presented by Glowinski, Pan, Hesla and Joseph (1999). An important feature of this finite element based method is that the flow in the particle domain is constrained to be a rigid body motion by using a well-chosen field of Lagrange multipliers. The ...

We study the problem of multicut segmentation. We introduce modified versions of the Semi-PlanarCC based on bounding Lagrange multipliers. We apply our work to natural image segmentation.

This paper presents a novel approach to implement the interpolation function by means of Lagrange interpolators. The proposed architecture does not require high-frequency multipliers. With respect to conventional sinc filters of a comparable order, the response of Lagrange interpolators is better both in the passband and in the stopband, while the proposed implementation requires only a small i...

The mortar nite element method allows the coupling of diierent discretization schemes and triangulations across subregion boundaries. In the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modiied trace space which serves as a space of Lagrange multipliers. In this paper, this Lagrange multiplier space is replaced ...

Assuming that the primal part of the sequence generated by a Newton-type (e.g., SQP) method applied to an equality-constrained problem converges to a solution where the constraints are degenerate, we investigate whether the dual part of the sequence is attracted by those Lagrange multipliers which satisfy second-order sufficient condition (SOSC) for optimality, or by those multipliers which vio...

We propose a new method for making the inventory replenishment decisions in distribution systems. In particular, we consider distribution systems consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. The method that we propose is based on formulating the distribution problem as a dynamic program and relaxing the constraints that ensure the nonnega...

In the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [12]. A least-squares method is presented here for mesh tying in the p...