Semistrict G-Preinvexity and Optimality in Nonlinear Programming
نویسندگان
چکیده
and Applied Analysis 3 Proof. Let x, y ∈ K. From the assumption of f(y+η(x, y)) ≤ f(x), when λ = 0, 1, we can know that f (y + λη (x, y)) ≤ G −1 (λG (f (x)) + (1 − λ)G (f (y))) . (9) Then, there are two cases to be considered. (i) Iff(x) ̸ = f(y), then by the semistrictG-preinvexity of f, we have the following:
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*Correspondence: [email protected] 1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China Full list of author information is available at the end of the article Abstract With the equivalent relationships between the G-generalized invexities and general invexities on the hand, we present two characterizations for G-preinvexity; we also discuss the relationships...
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