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Smoothing by mollifiers. Part II: nonlinear optimization

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Abstract

This article complements the paper (Jongen, Stein, Smoothing by mollifers part I: semi-infinite optimization J Glob Optim doi:10.1007/s10898-007-9232-3), where we showed that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. In the special case of nonlinear programming this function is constructed as the mollification of the finite min-function which describes the feasible set. In the present article we treat the correspondences between Karush–Kuhn–Tucker points of the original and the smoothed problem, and between their associated Morse indices.

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Authors and Affiliations

  1. Department of Mathematics – C, RWTH Aachen University, 52056, Aachen, Germany

    Hubertus Th. Jongen

  2. School of Economics and Business Engineering, University of Karlsruhe, 76128, Karlsruhe, Germany

    Oliver Stein

Authors
  1. Hubertus Th. Jongen
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  2. Oliver Stein
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Correspondence to Oliver Stein.

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Jongen, H.T., Stein, O. Smoothing by mollifiers. Part II: nonlinear optimization. J Glob Optim 41, 335–350 (2008). https://doi.org/10.1007/s10898-007-9231-4

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  • DOI: https://doi.org/10.1007/s10898-007-9231-4

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