Summary
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.
Research supported by NSF Grant ECS-0218328.
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Bertsekas, D.P. (2006). Lagrange Multipliers with Optimal Sensitivity Properties in Constrained Optimization. In: Di Pillo, G., Roma, M. (eds) Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications, vol 83. Springer, Boston, MA. https://doi.org/10.1007/0-387-30065-1_2
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DOI: https://doi.org/10.1007/0-387-30065-1_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30063-4
Online ISBN: 978-0-387-30065-8
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