We present an elementary self-contained proof for the Lagrange multiplier rule. It does not refer to any substantial preparations and it is only based on the observation that a certain limit is positive. At the end of this note, the power of the Lagrange multiplier rule is analyzed.

It is crucial to maximize marketing efficiency and customer satisfaction in personalized marketing. In this paper, we raise the multiple recommendation problem which occurs when performing several personalized campaigns simultaneously. We formulate the multi-campaign assignment problem to solve this issue and propose methods for solving the problem. The most notable element is the Lagrange mult...

The Variational Iteration Method (VIM) is an iterative method that approximates solutions of differential equations. The method is a modification of the so-called general Lagrange multipliers [2]. The method is based on the idea of constructing a correction functional that uses a Lagrange multiplier. In this study, we analyse some basic properties of the Lagrange multiplier; and using these, we...

In this paper, we propose a field redefinition invariant Lagrange multiplier (LM) formalism in which new ghost-like fields, analogous to Lee-Yang ghosts, are introduced. These ghost fields required restore the invariance of standard path integral LM theory and, at same time, cancel additional contributions due fields. We argue that extra degrees freedom formalism, coming from should against Hen...

In the Fictitious Domain Method with Lagrange multiplier (FDM) the physical domain is embedded into a simpler but larger domain called the fictitious domain. The partial differential equation is extended to the fictitious domain using a Lagrange multiplier to enforce the prescribed boundary conditions on the physical domain while all the other data are extended to the fictitious domain. This le...