We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi’s method by applying it to the same equation studied by Musielak et al. with their own method [Musielak ZE, Roy D and Swift LD. Method to derive Lagrangian and Hamiltonian for a nonlinear dynami...

It is well known that the conventional edge element method in solving vector Maxwell’s eigenvalue problem will lead to the presence of nonphysical zero eigenvalues. This paper uses the mixed finite element method to suppress the presence of these nonphysical zero eigenvalues for 2D vector Maxwell’s eigenvalue problem in anisotropic media. We introduce a Lagrangian multiplier to deal with the co...

The Lees–Edwards description of bi-periodic boundary conditions has been extended to the streamfunction and streamfunction–vorticity formulation in sliding bi-periodic frames. The required compatibility conditions are formulated and uniqueness of the solution is shown. The model has been implemented in a spectral element method context to describe bulk shear behavior far away from walls, where ...

We introduce the “sample” technique to generate robust critical values for the Jarque and Bera (JB) Lagrangian Multiplier (LM) test for normality, JBCV( 1 2 , k k ), by using improved critical values the true size of the test approaches its nominal value. Monte Carlo methods are used to study the size, and the power of the JB normality test with the “sample” critical values and compare with thr...

A minimax duality for a Gaussian mutual information expression was introduced by Yu. An interesting observation is the relationship between cost constraints on the transmit covariances and noise covariances in the dual problem via Lagrangian multipliers. We introduce a minimax duality for general MIMO interference networks, where noise and transmit covariances are optimized subject to linear co...

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...

Due to irregular operations, the crew cost at the end of a month is typically substantially higher than the projected crew cost in planning. We assume that the fleeting and the aircraft routing decisions have already been made. We present a model and a solution methodology that produces robust crew schedules in planning. Besides the objective of minimizing the crew cost, we introduce the object...