Second-order characterization of convex mappings in Banach spaces and its applications

Mohammad Taghi Nadi () and Jafar Zafarani ()
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Mohammad Taghi Nadi: University of Isfahan
Jafar Zafarani: Sheikhbahaee University and University of Isfahan

Journal of Global Optimization, 2023, vol. 86, issue 4, No 9, 1005-1023

Abstract: Abstract We show that the positive semi-definiteness of the regular or limiting (Mordukhovich) second-order subdifferential of an approximately convex function is a sufficient condition for its convexity. As a consequence of our result, we obtain a second-order characterization for the class of lower- $$C^1$$ C 1 functions. Furthermore, we show by an example that positive semi-definiteness of the second-order subdifferential of convex functions is not a necessary condition for some cases. Also, a second-order characterization for C-convex mappings is obtained, and derive some applications in optimization.

Keywords: Convex function; Locally Lipschitz; Lower- $$C^1$$ C 1 function; Second-order subdifferential; Convex mapping; Vector optimization; 26B25; 47H04; 49J52; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01301-z

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