On Second-Order Generalized Convexity

C. Zălinescu ()
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C. Zălinescu: University Alexandru Ioan Cuza

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 5, 802-829

Abstract: Abstract Second-order convex functions were introduced by Mond (Opsearch 11(2–3):90–99, 1974) in order to deal with second-order duality. Then that notion was generalized again and again, using more and more parameters introduced using several quantifiers. In the present paper, we show that most of these notions have quite simple intrinsic characterizations. This paper can be viewed as a continuation of our paper (Zălinescu in An Ştiinţ Univ Al I Cuza Iaşi Secţ I a Mat 35(3):213–220, 1989) in which we characterized generalized bonvex functions.

Keywords: Second-order (generalized) convex function; Semidefinite matrix; Quadratic function; 26B25; 90C26 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0820-y

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