New Notions of Proper Efficiency in Set Optimization with the Set Criterion
本文针对集合优化问题，基于集合解准则引入了Henig意义上的适当有效性新概念，研究了它们之间的关系，并与向量准则下的概念进行了比较，最后在凸性假设下得到了带锥约束的集合优化问题的拉格朗日乘子规则。
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.