Set-valued parametric optimization problems with higher-order ρ-cone arcwise connectedness

• Koushik Das ^[1]
  1. [1] Department of Mathematics, Taki Government College
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 4, 2024, págs. 589-607
• Idioma: inglés
• DOI: 10.1007/s40324-023-00344-2
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• Resumen

  • In this study, we take into account the set-valued parametric optimization problem (PP) (abbreviated as SVPOP), in which both the objective and constraint maps are set-valued. In order to generalize higher-order cone arcwise connected set-valued maps, we develop the idea of higher-order ρ-cone arcwise connectedness of set-valued maps. Under higher-order contingent epiderivative and higher-order ρ-cone arcwise connectivity assumptions, we provide higher-order sufficient Karush-Kuhn-Tucker (KKT) optimality criteria for the problem (PP). In addition, we investigate higher-order Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and establish the corresponding higher-order weak, strong, and converse duality theorems between the primal problem (PP) and analogous dual problems under the presumption of higher-order ρ-cone arcwise connectedness.