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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the algebraic criteria for local Pareto optima. II
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by Yieh Hei Wan
Trans. Amer. Math. Soc. 245 (1978), 385-397
DOI: https://doi.org/10.1090/S0002-9947-1978-0511417-1
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Abstract:

Constrained vector optimization problems in the large are studied in this paper. Fixing any constraints so that the feasible set is a manifold with corners, we prove that the set of local Pareto optima for typical vector-valued functions admit Whitney prestratifications. Furthermore, these prestratifications persist under small perturbation of vector-valued functions. The main tools used here are a variant of Thom’s transversality theorem and the stratification theory of semialgebraic sets.
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Bibliographic Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 245 (1978), 385-397
  • MSC: Primary 58E17; Secondary 58C27, 90A14
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0511417-1
  • MathSciNet review: 511417