Generalized ( ,α, ρ, θ)–d–V–univex functions and non-smooth alternative theorems
Zishuang Tong, X. J. Zheng · International Journal of Computer Mathematics · 2008
Under a new kind of generalized convexity and non-smooth generalized (, α, ρ, θ)–d–V–univexity, some basic alternative theorems are established and proved. These results extend some other generalized convex alternative theorems. To illustrate their applications, we present characterizations of saddle-point type necessary optimality conditions for properly efficient solutions of vector optimization problems. To conclude, the alternative theorems are applied to yield a canonical convex alternative theorem as a corollary.