Abstract
First-order and second-order optimality conditions for the infinite-dimensional mathematical programming problem are given. The necessary conditions are an immediate generalization of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions. Here to go from finite to infinite dimensions results in an essential change. It is the aim of this paper to show where this is caused by and to develop modified sufficient optimality conditions for the infinite-dimensional situation. In particular it turns out that the somewhat artificially looking second-order conditions we gave in [5] are a quite natural consequence of the sufficient first-order conditions.
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© 1978 Springer-Verlag Berlin Heidelberg
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Zowe, J., Maurer, H. (1978). Optimality Conditions for the Programming Problem in Infinite Dimensions. In: Henn, R., Korte, B., Oettli, W. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95322-4_27
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DOI: https://doi.org/10.1007/978-3-642-95322-4_27
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