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Transactions of the American Mathematical Society

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

 

 

On the algebraic criteria for local Pareto optima. II


Author: Yieh Hei Wan
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
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0511417-1
Keywords: Local Pareto optima, Whitney prestratification, semialgebraic sets, Thom's transversality theorem
Article copyright: © Copyright 1978 American Mathematical Society