Second-order optimality conditions for cone-subarcwise connected set-valued optimization problems

Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness

“…Definition 5 (Fu and Wang, 2003;Lalitha et al, 2003) Let A be an arcwise connected subset of a real normed space U and F : U → 2 V be a set-valued map, with A ⊆ dom(F). Then F is said to be Ω-arcwise connected on A if Peng and Xu (2018) introduced the notion of cone subarcwise connected set-valued maps.…”

“…Definition 6 (Peng and Xu, 2018) Let A be an arcwise connected subset of a real normed space U , e ∈ int(Ω), and F : U → 2 V be a set-valued map, with A ⊆ dom(F). Then, F is said to be Ω-subarcwise connected on A if…”

“…Yu (2016) established the necessary and sufficient optimality conditions for global proper efficient element in vector optimization problem with cone arcwise connected set-valued maps. In 2018, Peng and Xu (2018) introduced the notion of cone subarcwise connected set-valued maps and established the second-order necessary optimality conditions for local global proper efficient elements of set-valued optimization problems.…”

On Constrained Set-Valued Semi-Infinite Programming Problems with ρ-Cone Arcwise Connectedness

“…Peng and Xu [16] introduced the notion of cone subarcwise connectedness of setvalued maps. Definition 6 ([16]).…”

“…Yu [15] established the necessary and sufficient optimality conditions for the existence of global proper efficient elements in vector optimization problems. In 2018, Peng and Xu [16] introduced the notion of cone subarcwise connected set-valued maps. They also established the second-order necessary optimality conditions for global proper efficiency of set-valued optimization problems.…”