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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 73 (1992), S. 101-120 
    ISSN: 1573-2878
    Keywords: Marginal function ; differential stability ; generalized gradients ; tangent cones ; exact penalty functions ; constraint qualifications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 80 (1994), S. 551-571 
    ISSN: 1573-2878
    Keywords: Strict local minimizers of orderm ; optimality conditions ; C 1,1 functions ; tangent cones ; weak sharp local minimizers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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