A Lagrangian based heuristic is proposed for many-to-many assignment problems taking into account capacity limits for task and agents. A modified Lagrangian bound studied earlier by the authors is presented and a greedy heuristic is then applied to get a feasible Lagrangian-based solution. The latter is also used to speed up the subgradient scheme to solve the modified Lagrangian dual problem. ...

Taking the Stückelberg Lagrangian associated with the abelian selfdual model of P. K. Townsend et al as a starting point, we embed this mixed firstand second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example...

The first Lagrangian Analysis and Predictability of Coastal and Ocean Dynamics (LAPCOD) meeting took place in Ischia, Italy, 2–6 October 2000. The material presented at LAPCOD 2000 indicated both a maturing of Lagrangian-based observing systems and the development of new analysis and assimilation techniques for Lagrangian data. This summary presents a review of the state-of-the-art technology i...

We present a discrete analog of the recently introduced Hamilton– Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete Lagrangian to define a finite version of Hamilton’s action principle, or treating it as a symplectic generating function. This is demonstrated for a discrete Lagra...

We investigate the extrinsic topology of Lagrangian submanifolds and of their submanifolds in closed symplectic manifolds using Floer homological methods. The first result asserts that the homology class of a displaceable monotone Lagrangian submanifold vanishes in the homology of the ambient symplectic manifold. Combining this with spectral invariants we provide a new mechanism for proving Lag...

A proof is given for the observation that the equations of motion for the companion Lagrangian without a square root, subject to some constraints, just reduce to the equations of motion for the companion Lagrangian with a square root in one less dimension. The companion Lagrangian is just an extension of the Klein-Gordon Lagrangian to more fields in order to provide a field description for stri...

In this work, we consider multigoal-oriented error estimation for stationary fluid–structure interaction. The problem is formulated within a variational-monolithic setting using arbitrary Lagrangian–Eulerian coordinates. Employing the dual-weighted residual method goal-oriented posteriori estimation, adjoint sensitivities are required. For combined functional such that several quantities of int...

A. This article address two issues. First, we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] an isomorphism between Hamiltonian Floer homology and singular homology is established. In contrast, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian submanifold,...

The motion of a mechanical system is related via a set of dynamic equations to the forces and torques it is subject to. In this work we will be primarily interested in robots consisting of a collection of rigid links connected through joints that constrain the relative motion between the links. There are two main formalisms for deriving the dynamic equations for such mechanical systems: (1) New...

We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem...