Cone arcwise connectivity in optimization problems with difference of set-valued mappings

• Koushik Das ^[1] ; Izhar Ahmad ^[2] ; Savin Treanţă ^[3]
  1. [1] Department of Mathematics, Taki Government College
  2. [2] Department of Mathematics, King Fahd University of Petroleum & Minerals
  3. [3] Department of Applied Mathematics, University Politehnica of Bucharest

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 3, 2024, págs. 511-529
• Idioma: inglés
• DOI: 10.1007/s40324-023-00338-0
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  • By using ρ cone arcwise connectivity and contingent epi-derivative suppositions, we show the circumstances of sufficiency of the Karush-Kuhn-Tucker type for an optimization problem having the objective mappings and the associated constraints as the difference of set-valued mappings. We also prove the analogous weak, converse, and strong dualities for the Wolfe-type dual of the optimization problem. To back up our findings, we present several instances. Our conclusions reduce to those of optimization problems as the difference of scalar-valued mappings as a particular instance.