Error estimates are derived for an augmented Lagrangian approximation to an optimal control problem. Convex control constraints are treated explicitly while a Lagrange multiplier is introduced for the nonlinear system dynamics. The nonlinear optimal control problem does not fit the classical theory for estimating the error in multiplier approximations, since the natural coercivity assumption is...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

General Relativity is a background independent theory which identify the gravitational interaction into the metric properties of the space-time and this peculiar nature makes very subtle even simple questions about its quantization. To deal with a canonical method for the fields dynamics necessarily involves the notion of a physical time variable, whose conjugate momentum fixes the Hamiltonian ...

The Lagrangian coder control together with the parameter choice is presented that lead to the creation of the new hybrid video coder specifications TMN-10 for H.263 and TML for H.26L. An efEcient approach for the determination of the encoding parameters is developed. It is shown by means of experimental results that the Lagrange multiplier for the macroblock mode decision corre sponds to the ne...

This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from U-Lagrangian theory and from Riemannian geometry. The Hessian based on the ULagrangian depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for wh...

We present a Lorentz invariant lagrangian formulation for a supersymmetric Yang-Mills vector multiplet in eleven dimensions (11D). The Lorentz symmetry is broken at the field equation level, and therefore the breaking is spontaneous, as in other formulations of supersymmetric theories in 12D or higher dimensions. We introduce a space-like unit vector formed by the gradient of a scalar field, av...

A power control scheme for packet-based wireless communication systems is proposed in this paper. The proposed power control scheme aims at minimizing the total number of transmission that a packet needs before it is received successfully over a Rayleigh fading channel subject to two constraints. One is that the transmission power should be greater than zero. The other is imposed by the constra...

We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds P and Q of a manifold M endowed with a distribution D ⊂ TM. We give a different proof, that holds in a more general context, of a result by Bismut [2, Theorem 1.17] stating that the normal extremizers that are not abnormal are critical points of the sub-Riemannian action functio...

Coupling methods for continuum models with molecular models are developed. Two methods are studied here: an overlapping domain decomposition method, which has overlapping domain, and an edge-to-edge decomposition method, which has an interface between two models. These two methods enforce the compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or t...