New Notions of Proper Efficiency in Set Optimization with the Set Criterion

L. Huerga (), B. Jiménez () and V. Novo ()
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L. Huerga: Universidad Nacional de Educación a Distancia (UNED)
B. Jiménez: Universidad Nacional de Educación a Distancia (UNED)
V. Novo: Universidad Nacional de Educación a Distancia (UNED)

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 3, No 6, 878-902

Abstract: Abstract In this paper, we introduce new notions of proper efficiency in the sense of Henig for a set optimization problem by using the set criterion of solution. The relationships between them are studied. Also, we compare these concepts with the homologous ones given by considering the vector criterion. Finally, a Lagrange multiplier rule for Henig proper solutions of a set optimization problem with a cone constraint is obtained under convexity hypotheses. Illustrative examples are also given.

Keywords: Set optimization; Set criterion of solution; Vector criterion of solution; Henig proper efficiency; Lagrange multipliers; 06A75; 49J53; 90C29 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02088-x

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