The well-known and established global optimality conditions based on the Lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero. We develop a set of global optimality conditions which are structurally similar but which are consistent for any size of the duality gap. This system characterizes a primal–dual optimal solution by means of primal and d...

Abstract Lagrangian models use calculus to solve multi-variable non-linear constrained optimization of problems and for identifying the marginal changes (‘shadow prices’) optimal solutions in constraint bounds. This is especially useful when constraints represent resource limitations.

| This paper describes two new xed-rate entropy-coded quantization methods for stationary memoryless sources where the structure of code-words are derived from a variable-length scalar quantizer. In the rst method, we formulate the quantization as a zero-one integer optimization problem. We show that the resulting integer program can be closely approximated by solving a simple linear program. T...

We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behavior at space infinity in the asymptotically flat case is identical to other alternative Lagrangians for General Relativity, like the gamma-gamma Lagrangian used by Einstein. We develop...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate 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 fami...

In this paper we consider the single machine scheduling problem with precedence constraints to minimize the total weighted tardiness of jobs. This problem is known to be strongly NP-hard.A solution methodology based on Lagrangian relaxation is developed to solve it. In this approach, a hybrid backward and forward dynamic programming algorithm is designed for the Lagrangian relaxed problem, whic...

The multiclass Lighthill-Whitham-Richards (MCLWR) traffic model, which distinguishes N classes of drivers differing in preferential velocity, gives rise to a system of N strongly coupled, nonlinear first-order conservation laws for the local car densities as a function of distance and time.We propose a new class of anti-diffusive schemes by splitting the system of conservation laws into two dif...

We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behavior at space infinity in the asymptotically flat case is identical to other alternative Lagrangians for General Relativity, like the gamma-gamma Lagrangian used by Einstein. We develop...

this work deals with effects of asymmetric stiffness on the dynamic behaviour of the rotor system. the analysis is presented through an extended lagrangian hamiltonian mechanics on the asymmetric rotor system, where symmetries are broken in terms of the rotor stiffness. the complete dynamics of asymmetries of rotor system is investigated with a case study. in this work, a mathematical model is ...