Lagrange multipliers and nonlinear programming

Dynamic Programming and Lagrange Multipliers.

Lagrange Multipliers and Optimality

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

The Theory of Discrete Lagrange Multipliers for Nonlinear Discrete Optimization

In this paper we present a Lagrange-multiplier formulation of discrete constrained optimization problems, the associated discrete-space first-order necessary and sufficient conditions for saddle points, and an efficient first-order search procedure that looks for saddle points in discrete space. Our new theory provides a strong mathematical foundation for solving general nonlinear discrete opti...

Interpretation of Lagrange multipliers in nonlinear pricing problem

We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization probl...

Substructuring by Lagrange Multipliers