Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1985-04-30
Mean Value Theorem for Functions Possessing First Order Convex Approximations. Applications in Optimization TheoryMarcin Studniarski (1) Uniwersytet Lodzki, Poland
A mean value theorem for functions possessing first order convex approximations in the sense of Ioffe  is derived. It comprises two known results for convex and locally Lipschitzian functions as particular cases. This theorem is used in order to obtain a sufficient condition for a function defined on the Cartesian product of two topological vector spaces to possess a first order convex approximation. Some applications in optimization theory are also given.
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Studniarski Marcin: Mean Value Theorem for Functions Possessing First Order Convex Approximations. Applications in Optimization Theory. Z. Anal. Anwend. 4 (1985), 125-132. doi: 10.4171/ZAA/142