The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin–Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.

这项工作的目的是研究按词典词典顺序排列的目标空间的优化相关问题，包括参数词典词典平衡问题和具有词典词典约束的优化问题。我们针对这些问题引入了Levitin–Polyak适定性的概念，并为此类性质建立了许多充分条件。这些假设直接施加在问题的数据上，并且确实可以验证。我们不需要假设解决方案集的存在（和/或凸性，紧致性），因为它是使用数据上提到的假设进行证明的。而且，我们的假设比通常施加的假设更为宽松。