On constrained set-valued optimization problems with $$\rho $$-cone arcwise connectedness

Das, Koushik

doi:10.1007/s40324-022-00295-0

Cited by 4 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a generalization of cone arcwisely connected SVMs, Das [12], and Das et al [17] presented the idea of σ-cone arcwisely connectedness of SVMs and subsequently derived the required optimality requirements for various types of SVOPs. Definition 2.12 [12,17] Let M be an arcwisely connected subset of a RNS α, e ∈ int(Q), and π : α → 2 β be a SVM, with M ⊆ domain(π). Then π is known as σ-Q-arcwisely connected w.r.t.…”

Section: Definition 210 [22]mentioning

confidence: 99%

Set-valued minimax programming problems under higher-order σ-arcwisely connectivity

DAS

2023

Preprint

Self Cite

View full text Add to dashboard Cite

In this work, a set-valued minimax programming problem (MP) is taken into account. In the broad sense of higher-order arcwisely connected set-valued maps, we introduce the concept of higher-order σ-arcwisely connectedness of set-valued maps. Under higher-order contingent epidifferentiation and higher-order σ-arcwisely connectivity suppositions, the higher-order sufficient criteria for Karush-Kuhn-Tucker (KKT) optimality are constructed for the problem (MP). Additionally, we develop the higher-order Mond-Weir, Wolfe, and mixed kinds of duality and demonstrate the higher-order strong, weak, and converse theorems of duality among our main problem (MP) and the associated duals under higher-order σ-arcwisely connectivity supposition. Mathematics Subject Classification (2000) 26B25 · 49N15

show abstract