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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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Preservation of convergence of convex sets and functions in finite dimensions
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by L. McLinden and Roy C. Bergstrom PDF
Trans. Amer. Math. Soc. 268 (1981), 127-142 Request permission

Abstract:

We study a convergence notion which has particular relevance for convex analysis and lends itself quite naturally to successive approximation schemes in a variety of areas. Motivated particularly by problems in optimization subject to constraints, we develop technical tools necessary for systematic use of this convergence in finite-dimensional settings. Simple conditions are established under which this convergence for sequences of sets, functions and subdifferentials is preserved under various basic operations, including, for example, those of addition and infimal convolution in the case of functions.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 268 (1981), 127-142
  • MSC: Primary 26B25; Secondary 65K10
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0628449-5
  • MathSciNet review: 628449