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  • 1
    Digitale Medien
    Digitale Medien
    Differential stability in non-Lipschitzian optimization (1992)
    Springer
    Journal of optimization theory and applications 73 (1992), S. 101-120 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Marginal function ; differential stability ; generalized gradients ; tangent cones ; exact penalty functions ; constraint qualifications
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, upper and lower bounds are established for the Dini directional derivatives of the marginal function of an inequality-constrained mathematical program with right-hand-side perturbations. A nonsmooth analogue of the Cottle constraint qualification is assumed, but the objective and constraint functions are not assumed to be differentiable, convex, or locally Lipschitzian. Our upper bound sharpens previous results from the locally Lipschitzian case by means of a subgradient smaller than the Clarke generalized gradient. Examples demonstrate, however, that a corresponding strengthening of the lower bound is not possible. Corollaries of this work include general criteria for exactness of penalty functions as well as information on the relationship between calmness and other constraint qualifications in nonsmooth optimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940081
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Characterizations of strict local minima and necessary conditions for weak sharp minima (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 551-571 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Strict local minimizers of orderm ; optimality conditions ; C 1,1 functions ; tangent cones ; weak sharp local minimizers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In nonlinear programming, sufficient conditions of orderm usually identify a special type of local minimizer, here termed a strict local minimizer of orderm. In this paper, it is demonstrated that, if a constraint qualification is satisfied, standard sufficient conditions often characterize this special sort of minimizer. The first- and second-order cases are treated in detail. Necessary conditions for weak sharp local minima of orderm, a larger class of local minima, are also presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02207780
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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