Abstract
This paper introduces seven derivatives in mathematical programming in locally convex topological vector spaces. All these derivatives have been known in various fields of mathematical sciences but they have never been used before in mathematical programming. The weakest of the seven derivatives is the compact derivative of Gil de Lamadrid and Sova. The derivative used by Neustadt in optimization theory is stronger than the compact derivative and it is equivalent to the derivative introduced by Michal and Bastiani. The main results of the paper show that the optimality conditions of both Lagrange—Kuhn—Tucker type and Caratheodory—John type hold for compactly differentiable functions. In the case of finite-dimensional spaces all these seven derivatives are equivalent to the Fréchet derivative.
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Massam, H., Zlobec, S. Various definitions of the derivative in mathematical programming. Mathematical Programming 7, 144–161 (1974). https://doi.org/10.1007/BF01585512
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DOI: https://doi.org/10.1007/BF01585512