Lagrange Murderpliers Done Correctly
نویسنده
چکیده
Lagrange multipliers offer a way to find the extrema of an objective function f(x1, x2, . . . , xn) subject to a constraint function g(x1, x2, . . . , xn) = 0; for example, we may wish to maximize a+ b+ c subject to a2 + b2 + c2 = 1. However, there are lots of tiny details that need to be checked in order to completely solve a problem with Lagrange multipliers. On an olympiad the use of Lagrange multipliers is almost certain to draw the wrath of graders, so it is imperative that all these details are done correctly.
منابع مشابه
A FETI-DP Formulation for Two-dimensional Stokes Problem on Nonmatching Grids
We consider a FETI-DP formulation of the Stokes problem with mortar methods. To solve the Stokes problem correctly and efficiently, redundant continuity constraints are introduced. Lagrange multipliers corresponding to the redundant constraints are treated as primal variables in the FETI-DP formulation. We propose a preconditioner for the FETI-DP operator and show that the condition number of t...
متن کاملSymmetric Criticality in Classical Field Theory
This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields ...
متن کاملGeneralized Companion Matrices in the Lagrange Basis
It is well known that solving polynomial equations, or finding the eigenvalues of matrix polynomials, can be done by transforming to a generalized eigenvalue problem (see for example [10]). In this paper we examine a new way to do this directly from the values of the polynomial or matrix polynomial at distinct evaluation points.
متن کاملDynamic Analysis of Dam-Reservoir Interaction in Time Domain
In the present paper, some finite element softwares about interaction of dam and reservoir during earthquake in time domain are discussed. Impedance option is used as boundary condition of absorbent of reservoir and wave. For each software, time history analysis of pressure and displacement are done and finally suitable elements for dam structure and reservoir fluid are introduced comparing the...
متن کاملAnalog Circuits for Constrained Optimization
This paper explores whether analog circuitry can adequately perform constrained optimization. Constrained optimization circuits are designed using the differential multiplier method. These circuits fulfill time-varying constraints correctly. Example circuits include a quadratic programming circuit and a constrained flip-flop.
متن کامل