New Notions of Proper Efficiency in Set Optimization with the Set Criterion
Lidia Huerga, Bienvenido Jiménez, Vicente Novo · Journal of Optimization Theory and Applications · 2022
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.