Abstract
In this study, we develop general optimality conditions of both Fritz John and Kuhn-Tucker type for an optimization problem with nondifferentiable data. The already known conditions are sharpened by considering globally the vector-valued function defined by all the functions involved in the problem. The multipliers for the constrained problem are constructed as limit values of multipliers for unconstrained perturbed versions of the problem. Regularity assumptions yielding Kuhn-Tucker type results are formulated in terms of constant rank condition, maximal rank condition, etc., for a subset of matrices associated to the data of the problem.
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Communicated by J. Stoer
This research was supported in part by the National Science Foundation under grant MCS 77-00241 while the author was on leave from the Université de Clermont II, France
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Hiriart-Urruty, J.B. Refinements of necessary optimality conditions in nondifferentiable programming I. Appl Math Optim 5, 63–82 (1979). https://doi.org/10.1007/BF01442544
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DOI: https://doi.org/10.1007/BF01442544