Lagrange Multipliers with Optimal Sensitivity Properties

  • Dimitri Bertsekas
    • Categories Constrained Nonlinear Optimization Tags , Short URL: https://optimization-online.org/?p=8977

    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.

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

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