196 research outputs found

    The Radius of Metric Subregularity

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    There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

    Complete Characterizations of Local Weak Sharp Minima With Applications to Semi-Infinite Optimization and Complementarity

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    In this paper we identify a favorable class of nonsmooth functions for which local weak sharp minima can be completely characterized in terms of normal cones and subdifferentials, or tangent cones and subderivatives, or their mixture in finite-dimensional spaces. The results obtained not only significantly extend previous ones in the literature, but also allow us to provide new types of criteria for local weak sharpness. Applications of the developed theory are given to semi-infinite programming and to semi-infinite complementarity problems

    Comparing Two Integral Means for Absolutely Continuous Mappings Whose Derivatives are in L∞[a,b] and Applications

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    Estimates of the difference of two integral means on [a,b], [c,d] with [c,d] ⊂ [a,b] in terms of the sup norm of the derivative and applications for pdfs, special means, Jeffreys’ divergence and continuous streams are given
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