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Transactions of the American Mathematical Society

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

 
 

 

The adjoint arc in nonsmooth optimization


Authors: Philip D. Loewen and R. T. Rockafellar
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1036004-7
Article copyright: © Copyright 1991 American Mathematical Society

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