Lagrange Multipliers with Optimal Sensitivity Properties

Dimitri Bertsekas (dimitribmit.edu)

Abstract: 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 constraint violation.

Keywords: Lagrange multiplier, sensitivity

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: MIT, Lab. for Information and Decision Systems Report 2632, October 2004

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Entry Submitted: 11/06/2004
Entry Accepted: 11/06/2004
Entry Last Modified: 11/06/2004

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