This paper is devoted to the autonomous Lagrange problem of the calculus of variations with a discontinuous Lagrangian. We prove that every minimizer is Lipschitz continuous if the Lagrangian is coercive and locally bounded. The main difference with respect to the previous works in the literature is that we do not assume that the Lagrangian is convex in the velocity. We also show that, under so...

We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900,Rl,2000. Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangia...

We study the global well-posedness of the Lagrangian averaged Euler equations in three dimensions. We show that a necessary and sufficient condition for the global existence is that the BMO norm of the stream function is integrable in time. We also derive a sufficient condition in terms of the total variation of certain level set functions, which guarantees the global existence. Furthermore, we...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with system lo...

Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP usin...

In this paper, we consider the working VP and backup VP routing problems jointly and employ the integer programming based approach to maximize the system resource utilization and the network survivability. The VP planning problem is formulated as a nonlinear combinatorial optimization problem. The objective function minimizes the resource usage while maximizing the network survivability. By pro...

This paper proposes an augmented Lagrangian Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN is the continuous Hopfield neural network based on augmented Lagrangian relaxation as its energy function. In the proposed ALHN, its energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagrangian re...

The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the Lagrangian L(v, x, t) from the set of orbits in Rn to a set of measure-valued orbits. The Eulerian, dual formulation leads an optimization problem on the set of sub-solutions of the corresponding Hamilton-Jacobi equation. Finally, the Monge proble...

The objective of this investigation is the establishment of governing balance and conservation laws in elastodynamics. The feature of the approach employed here consists in placing time on the same level as the space coordinates, as is done in the theory of relativity, i.e., pursuing a 4 · 4 formalism. Both the Lagrangian and the Eulerian descriptions of the postulated Lagrangian function are f...