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On the characterization of preinvex functions. (English) Zbl 1151.90033

The authors are interested in preinvex functions, a generalization of convex functions. In previous references, semi-strictly preinvex functions and strictly preinvex functions were characterized under restrictive conditions of lower and upper semi-continuity. It is noticed that these results can be retrieved, and sometimes generalized, under weaker assumptions.

MSC:

90C25 Convex programming
52A41 Convex functions and convex programs in convex geometry
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References:

[1] Yang, X.M., Li, D.: Semistrictly preinvex functions. J. Math. Anal. Appl. 258, 287–308 (2001) · Zbl 0985.26007
[2] Yang, X.M., Li, D.: On properties of preinvex functions. J. Math. Anal. Appl. 256, 229–241 (2001) · Zbl 1016.90056
[3] Weir, T., Mond, B.: Preinvex functions in multiple objective optimization. J. Math. Anal. Appl. 136, 29–38 (1988) · Zbl 0663.90087
[4] Luo, H.Z., Xu, Z.K.: On characterizations of prequasi-invex functions. J. Optim. Theory Appl. 120, 429–439 (2004) · Zbl 1100.90035
[5] Luo, H.Z., Wu, H.X., Zhu, Y.H.: Remarks on criteria of prequasi-invex functions. Appl. Math. J. Chin. Univ. 19, 335–341 (2004) · Zbl 1160.90662
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