Generalized (Phi, Rho)-convexity in nonsmooth vector optimization over cones
نویسندگان
چکیده
منابع مشابه
Higher-Order Minimizers and Generalized -Convexity in Nonsmooth Vector Optimization over Cones
In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results ar...
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and Applied Analysis 3 Definition 2.2 see 16 . Let ψ : R → R be a locally Lipschitz function, then ψ◦ u;v denotes Clarke’s generalized directional derivative of ψ at u ∈ R in the direction v and is defined as ψ◦ u;v lim sup y→u t→ 0 ψ ( y tv ) − ψ(y) t . 2.4 Clarke’s generalized gradient of ψ at u is denoted by ∂ψ u and is defined as ∂ψ u { ξ ∈ R | ψ◦ u;v ≥ 〈ξ, v〉, ∀v ∈ Rn}. 2.5 Let f : R → R b...
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ژورنال
عنوان ژورنال: An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
سال: 2016
ISSN: 2146-5703,2146-0957
DOI: 10.11121/ijocta.01.2016.00247