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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Necessary conditions for constrained optimization problems with semicontinuous and continuous data
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by Jonathan M. Borwein, Jay S. Treiman and Qiji J. Zhu PDF
Trans. Amer. Math. Soc. 350 (1998), 2409-2429 Request permission

Abstract:

We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.
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Additional Information
  • Jonathan M. Borwein
  • Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
  • Email: jborwein@cecm.sfu.ca
  • Jay S. Treiman
  • Affiliation: Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008
  • Email: treiman@math-stat.wmich.edu
  • Qiji J. Zhu
  • Affiliation: Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008
  • Email: zhu@math-stat.wmich.edu
  • Received by editor(s): September 14, 1995
  • Received by editor(s) in revised form: August 9, 1996
  • Additional Notes: Research of the first author was supported by NSERC and by the Shrum Endowment at Simon Fraser University
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2409-2429
  • MSC (1991): Primary 49J52; Secondary 49J40, 49J50, 58C20
  • DOI: https://doi.org/10.1090/S0002-9947-98-01984-9
  • MathSciNet review: 1433112