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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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The adjoint arc in nonsmooth optimization
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by Philip D. Loewen and R. T. Rockafellar
Trans. Amer. Math. Soc. 325 (1991), 39-72
DOI: https://doi.org/10.1090/S0002-9947-1991-1036004-7

Abstract:

We extend the theory of necessary conditions for nonsmooth problems of Bolza in three ways: first, we incorporate state constraints of the intrinsic type $x(t) \in X(t)$ for all $t$; second, we make no assumption of calmness or normality; and third, we show that a single adjoint function of bounded variation simultaneously satisfies the Hamiltonian inclusion, the Euler-Lagrange inclusion, and the Weierstrass-Pontryagin maximum condition, along with the usual transversality relations.
References
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Bibliographic Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 325 (1991), 39-72
  • MSC: Primary 49J52; Secondary 49K10
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1036004-7
  • MathSciNet review: 1036004