Abstract
In this paper, necessary optimality conditions for nonlinear programs in Banach spaces and constraint qualifications for their applicability are considered. A new optimality condition is introduced, and a constraint qualification ensuring the validity of this condition is given. When the domain space is a reflexive space, it is shown that the qualification is the weakest possible. If a certain convexity assumption is made, then this optimality condition is shown to reduce to the well-known extension of the Kuhn-Tucker conditions to Banach spaces. In this case, the constraint qualification is weaker than those previously given.
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Communicated by G. B. Dantzig
This work was supported in part by the Office of Naval Research, Contract Number N00014-67-A-0321-0003 (NRO 47-095).
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Gould, F.J., Tolle, J.W. Optimality conditions and constraint qualifications in Banach space. J Optim Theory Appl 15, 667–684 (1975). https://doi.org/10.1007/BF00935506
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DOI: https://doi.org/10.1007/BF00935506