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Criteria for generalized invex monotonicities. (English) Zbl 1132.90360
Summary: Under appropriate conditions, we establish that (i) if the gradient of a function is (strictly) pseudo-monotone, then the function is (strictly) pseudo-invex; (ii) if the gradient of a function is quasi-monotone, then the function is quasi-invex; and (iii) if the gradient of a function is strong pseudo-monotone, then the function is strong pseudo-invex.

MSC:
90C25 Convex programming
26B25 Convexity of real functions of several variables, generalizations
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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[1] Ruiz-Garzón, G.; Osuna-Gómez, R.; Rufián-Lizana, A., Generalized invex monotonicity, European journal of operational research, 144, 501-512, (2003) · Zbl 1028.90036
[2] Yang, X.M.; Yang, X.Q.; Teo, K.L., Generalized invexity and generalized invariant monotonicity, Journal of optimization theory and applications, 117, 607-625, (2003) · Zbl 1141.90504
[3] Mohan, S.R.; Neogy, S.K., On invex sets and preinvex functions, Journal of mathematical analysis and applications, 189, 901-908, (1995) · Zbl 0831.90097
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