Abstract
We prove necessary extremum conditions for general nonlinear optimization problems in ordered topological vector spaces. For that reason, we define variational derivatives of higher order and introduce proper variations. Especially assuming certain weak hypotheses, we establish maximum principles of higher order.
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Communicated by G. Leitmann
This paper was developed within the FNK-sponsored Forschungsprojektschwerpunkt, Approximations in Optimization and Control Theory, WE 03, Fachbereich 19, Free University of Berlin, Berlin, Germany.
The authors wish to thank the referee, who has pointed out to them the papers of Krener (Ref. 28) and Virsan (Ref. 29). Both papers use methods which are similar to those presented here. However, because of the differences in the assumptions, the results cannot be compared directly.
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Hoffmann, K.H., Kornstaedt, H.J. Higher-order necessary conditions in abstract mathematical programming. J Optim Theory Appl 26, 533–568 (1978). https://doi.org/10.1007/BF00933151
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DOI: https://doi.org/10.1007/BF00933151