Generalized $${\varepsilon }$$ ε -quasi solutions of set optimization problems

C. Gutiérrez (), Rigoberto Lopez and J. Martínez ()
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C. Gutiérrez: University of Valladolid
J. Martínez: Universidad de Tarapacá

Journal of Global Optimization, 2022, vol. 82, issue 3, No 6, 559-576

Abstract: Abstract We introduce notions of generalized $$\varepsilon $$ ε -quasi solutions to approximate set type solutions of set optimization problems. We study their properties, consistency and limit behavior as approximations to efficient and strict weak efficient solutions. Moreover, we prove an existence result for such solutions and a bound for their asymptotic cone. Finally, we obtain optimality conditions for them.

Keywords: Set optimization; Approximate solution; Generalized $$\varepsilon $$ ε -quasi solution; Asymptotic map; Optimality condition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01098-9

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