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.


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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[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
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