## On the relationships between $$G$$-preinvex functions and semistrictly $$G$$-preinvex functions.(English)Zbl 1154.90010

Authors’ abstract: A new class of functions, termed semistrictly $$G$$-preinvex functions, is introduced in this paper. The relationships between semistrictly $$G$$-preinvex functions and $$G$$-preinvex functions are investigated under mild assumptions. Our results improve and extend the existing ones in the literature.

### MSC:

 90C26 Nonconvex programming, global optimization 26B25 Convexity of real functions of several variables, generalizations
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### References:

 [1] Antczak, T., $$r$$-pre-invexity and $$r$$-invexity in mathematical programming, Comput. math. appl., 50, 551-566, (2005) · Zbl 1129.90052 [2] Antczak, T., $$G$$-pre-invex functions in mathematical programming, J. comput. appl. math., (2007) · Zbl 1138.90027 [3] Antczak, T., New optimality conditions and duality results of $$G$$-type in differentiable mathematical programming, Nonlinear anal., 66, 1617-1632, (2007) · Zbl 1143.90034 [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. Chinese univ., 19, 335-341, (2004) · Zbl 1160.90662 [6] Pini, R., Invexity and generalized convexity, Optimization, 22, 513-525, (1991) · Zbl 0731.26009 [7] Weir, T.; Mond, B., Pre-invex functions in multiple objective optimization, J. math. anal. appl., 136, 29-38, (1988) · Zbl 0663.90087 [8] Yang, X.M.; Li, D., On properties of preinvex functions, J. math. anal. appl., 256, 229-241, (2001) · Zbl 1016.90056 [9] Yang, X.M.; Li, D., Semistrictly preinvex functions, J. math. anal. appl., 258, 287-308, (2001) · Zbl 0985.26007 [10] Yang, X.M.; Yang, X.Q.; Teo, K.L., Characterizations and applications of prequasi-invex functions, J. optim. theory appl., 110, 645-668, (2001) · Zbl 1064.90038
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