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Smooth positive extensions and nonlinear programming

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Abstract

We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York

    N. B. Waite (Research Staff Member)

Authors
  1. N. B. Waite
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Additional information

Communicated by R. A. Tapia

This paper is dedicated to the memory of Emily Sue Merkle Waite, Ph.D.

The author wishes to thank W. Cunningham for suggesting the question about constraint qualifications, A. Karr for noticing the example of a Brownian motion sample path, R. Byrd and P. Hartman for discussions, and E. Waite for support and encouragement.

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Waite, N.B. Smooth positive extensions and nonlinear programming. J Optim Theory Appl 80, 537–549 (1994). https://doi.org/10.1007/BF02207779

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  • DOI: https://doi.org/10.1007/BF02207779

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