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Marginal values and second-order necessary conditions for optimality

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Abstract

Second-order necessary conditions in nonlinear programming are derived by a new method that does not require the usual sort of constraint qualification. In terms of the multiplier vectors appearing in such second-order conditions, an estimate, is obtained for the generalized subgradients of the optimal, value function associated with a parameterized nonlinear programming problem. This yields estimates for ‘marginal values’ with respect to the parameters. The main theoretical tools are the augmented Lagrangian and, despite the assumption of second-order smoothness of objective constraints, the subdifferential calculus that has recently been developed for nonsmooth, nonconvex functions.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, USA

    R. Tyrrel Rockafellar

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  1. R. Tyrrel Rockafellar
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Additional information

Research sponsored in part by the Air Force Office of Scientific, Research, Air Force Systems Command United States Air Force, under grant No. F4960-82-k-0012.

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Tyrrel Rockafellar, R. Marginal values and second-order necessary conditions for optimality. Mathematical Programming 26, 245–286 (1983). https://doi.org/10.1007/BF02591866

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  • DOI: https://doi.org/10.1007/BF02591866

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