×

Semi-B-preinvex functions. (English) Zbl 1139.26006

Summary: In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions [X.Q.Yang and G.–Y.Chen, J. Math.Anal.Appl.169, No.2, 359–373 (1992; Zbl 0779.90067)] and the B-vex functions [J. Optim.Theory Appl.71, No.2, 237–253 (1991; Zbl 0793.90069)], is introduced. Examples are given to show that there exist functions which are semi-B-preinvex functions, but are neither semipreinvex nor B-vex. A property of the semi-B-preinvex functions is obtained.

MSC:

26B25 Convexity of real functions of several variables, generalizations
90C26 Nonconvex programming, global optimization
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hanson, M. A., On Sufficiency of the Kuhn Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29–38, 1981. · Zbl 0463.90080
[2] Craven, B. D., Invex Functions and Constrained Local Minima, Bulletin of the Australian Mathematical Society, Vol. 24, pp. 357–366, 1981. · Zbl 0452.90066
[3] Weir, T., and Mond, B., Preinvex Functions in Multiple-Objective Optimization, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29–38, 1988. · Zbl 0663.90087
[4] Weir, T., and Jeyakumar, V., A Class of Nonconvex Functions and Mathematical Programming, Bulletin of the Australian Mathematical Society, Vol. 38, pp. 177–189, 1988. · Zbl 0639.90082
[5] Yang, X. Q., and Chen, G. Y., A Class of Nonconvex Functions and Prevariational Inequalities, Journal of Mathematical Analysis and Applications, Vol. 169, pp. 359–373, 1992. · Zbl 0779.90067
[6] Bector, C. R., and Singh, C., B-Vex Functions, Journal of Optimization Theory and Applications, Vol. 71, pp. 237–253, 1991. · Zbl 0793.90069
[7] Bector, C. R., Suneja, S. K., and Lalitha, C. S., Generalized B-Vex Functions and Generalized B-Vex Programming, Journal of Optimization Theory and Applications, Vol. 76, pp. 561–576, 1993. · Zbl 0802.49027
[8] Suneja, S. K., Singh, C., and Bector, C. R., Generalization of Preinvex and B-Vex Functions, Journal of Optimization Theory and Applications, Vol. 76, pp. 577–587, 1993. · Zbl 0802.49026
[9] Yang, X. M., and Li, D., On Properties of Preinvex Functions, Journal of Mathematical Analysis and Applications, Vol. 256, pp. 229–241, 2001. · Zbl 1016.90056
[10] Peng, J. W., and Long, X. J., A Remark on Preinvex Functions, Bulletin of the Australian Mathematical Society, Vol. 70, pp. 397–400, 2004. · Zbl 1152.90569
[11] Yang, X. M., Yang, X. Q., and Teo, K. L., On Properties of Semipreinvex Functions, Bulletin of the Australian Mathematical Society, Vol. 68, pp. 449–459, 2003. · Zbl 1176.90475
[12] Yang, X. M., Yang, X. Q., and Teo, K. L., Explicitly B-Preinvex Functions, Journal of Computational and Applied Mathematics, Vol. 146, pp. 25–36, 2002. · Zbl 0999.26009
[13] Castagnoli, E., and Mazzolenl, P., About Derivatives of Some Generalized Concave Functions, Journal of Information and Optimization Sciences, Vol. 10, pp. 53–65, 1989. · Zbl 0681.90067
[14] Ben-Israel, A., and Mond, B., What Is Invexity?, Journal of the Australian Mathematical Society, Vol. 28, pp. 1–9, 1986. · Zbl 0603.90119
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.