Criticality of Lagrange multipliers in extended nonlinear optimization

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...

Lagrange Multipliers with Optimal Sensitivity Properties in Constrained Optimization

We consider optimization problems with inequality and abstract set constraints, and we derive sensitivity properties of Lagrange multipliers under very weak conditions. In particular, we do not assume uniqueness of a Lagrange multiplier or continuity of the perturbation function. We show that the Lagrange multiplier of minimum norm defines the optimal rate of improvement of the cost per unit co...

Theory of Lagrange Multipliers for Constrained Optimization Problems

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Substructuring by Lagrange Multipliers