A New Type of Directional Regularity for Mappings and Applications to Optimization
本文引入并研究映射的一种新型方向正则性，利用最小时间函数定义方向线性开性、度量正则性和Aubin性质三元组，提出方向Ekeland变分原理，给出方向正则性的充要条件，并应用于带函数目标的优化问题。
In this work we introduce and study a new type of directional regularity for mappings, making use of a minimal time function analyzed by the authors in a previous work. The corresponding directional triplet of linear openness, metric regularity, and Aubin property naturally appears, as shown by several examples. Then we devise a new directional Ekeland variational principle, which we use, along with other tools, to obtain necessary and sufficient conditions for directional regularity, formulated in terms of generalized differentiation objects. Finally, we apply the machinery developed before to the study of optimization problems with functional objectives.