Lagrange Multiplier

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations. A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two non-standard formulations, that numerous FV schemes, including

For many water authorities worldwide, one of the greatest potential areas for energy savings is in pump selection and in the related effective scheduling of daily pump operations. The optimal control and operation of an irrigation pumping station is achieved here by first solving the nonlinear governing model using Lagrange Multipliers (LM) and then through Genetic Algorithm (GA) approach. Computation

Abstract: In this paper, the direct differentiation method ͑DDM͒ for finite-element ͑FE͒ response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints ͑MPCs͒. The analytical developments are provided for three different constraint handling methods, namely: ͑1͒ the transformation equation method; ͑2͒ the Lagrange multiplier method; and ͑3͒ the penalty function method. Two nonlinear benchmark applications are presented: ͑1͒ a two-dimensional soil-foundation-structure interaction system and ͑2͒ a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDMbased response sensitivity results are compared with corres...

We use the meshless local Bubnov–Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations are shown to be stable, ...

We discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging (OWA) aggregation operator. The resulting weights are called the MEOWA weights. Using the method of LaGrange multipliers, we obtain an analytic form for these weights and describe some of their properties. The concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker's degree of optimism. This transformation, which is affected by an OWA ...

In this paper we try to provide additional insight into the problem of how to discriminate between the two most common spatial processes: the autoregressive and the moving average. This problem, whose analogous time series is apparently simple, acquires a certain complexity when it is considered in an irregular system of spatial units, mainly because there are few tools to carry out this discussion. Nevertheless, even with this lack, we believe that it is possible to make some progress using the methods available at present. In this paper we discuss the advantages and inconveniences of the different techniques that can help us to discriminate between both processes. We finish off the examination with a Monte Carlo exercise, and an application to the European regional income, which has enabled us to better understand the performance of several proposals such as the Lagrange Multipliers, the so-called Variance criterion and the tests of Vuong and Clarke.

The main aim of the present paper is to show how GLM method, as it was suggested by H. Everett, can be used in enumeration algorithm.
First of all we give a new optimality test. Though the test is a
general one, its use in integer programming is detailed. The existence
of gaps is the greatest difficulty of the GLM method. We show how
it can be avoided in integer programming. In the last section the
relation between the Lagrange multipliers and the surrogate
constraints is examined.

This report is the digitalized version of Problems of Control and Information Theory, 7(1978), 393-406. Only minimal changes
are done although the style of writing OR changed a lot since the time
of the original paper. Anything which were not contained in the original paper is in footnote.

A four-dimensional N=2 supersymmetric non-linear sigma-model with the Eguchi-Hanson (ALE) target space and a non-vanishing central charge is rewritten to a classically equivalent and formally renormalizable gauged `linear' sigma-model over a non-compact coset space in N=2 harmonic superspace by making use of an N=2 vector gauge superfield as the Lagrange multiplier. It is then demonstrated that the N=2 vector gauge multiplet becomes dynamical after taking into account one-loop corrections due to quantized hypermultiplets. This implies the appearance of a composite gauge boson, a composite chiral spinor doublet and a composite complex Higgs particle, all defined as the physical states associated with the propagating N=2 vector gauge superfield. The composite N=2 vector multiplet is further identified with the zero modes of a superstring ending on a D-6-brane. Some non-perturbative phenomena, such as the gauge symmetry enhancement for coincident D-6-branes and the Maldacena conjecture, turn out to be closely related to our NLSM via M-theory. Our results support a conjecture about the composite nature of superstrings ending on D-branes.

... 00207160902775090 Aldina Correia a * , João Matias b , Pedro Mestre c & Carlos Serôdio c pages 1841-1851. ... New York: IEOR Department, Columbia University. Mathematical Programming, Tech. Rep View all references, Fletcher et al. 66. Fletcher, R. and Leyffer, S. 1999. ...

The existence of the Pontryagin and Euler forms in a Weyl-Cartan space on the basis of the variational method with Lagrange multipliers are established. It is proved that these forms can be expressed via the exterior derivatives of the corresponding Chern-Simons terms in a Weyl-Cartan space with torsion and nonmetricity.

This paper details the use of automatic differentiation in form parameter driven curve design by constrained optimization. Computer aided design, computer aided engineering (CAD/CAE), and particularly computer aided ship hull design (CASHD) are typically implemented as interactive processes in which the user obtains desired shapes by manipulation of control vertices. A fair amount of trial and error is needed to achieve the desired properties. In the variational form parameter approach taken here, the system computes vertices so that the resulting curve meets the specifications and is optimized with respect to a fairness criteria. Implementation of curve design as an optimization problem requires extensive derivative calculations. The paper illustrates how the programming burden can be eased through the use of automatic differentiation techniques. A variational curve design framework has been implemented in Python, and applications to CASHD curve design are shown. The new method is robust and allows great flexibility in the selection of constraints. Offsets, tangents, and curvature may be imposed anywhere along the curve. Form parameters may also be used to define straight segments within a curve, require the curve to enclose specified forms, or specify relationships between curve properties.

In this study, the optimal placement of X steel diagonal braces (SDBs) is presented to upgrade the seismic response of a planar building frame. The optimal placement is defined as the optimal size and location of the SDBs in a frame structure. Steady state response of the structure evaluated at the undamped fundamental natural frequency is defined by means of

We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian system are subject to infinite conserved quantities due to the Vlasov dynamics. We show that the stationary states correspond to an extremum of the Boltzmann-Gibbs entropy, and their stability is obtained from the condition that this extremum is a maximum. As a consequence the entropy is a function of an infinite set of Lagrange multipliers that depend on the initial condition. We also discuss in this context the meaning of ensemble inequivalence and the temperature.