2018/12/31 by Thao, Nguyen Hieu, Bui, Hoa Thi, Cuong, Nguyen Duy +1
#FOS: Mathematics #Optimization and Control (math.OC) #Primary: 49J53 and 65K10. Secondary: 49K40 and 49M05 and 49M37 and 65K05 and 90C30
paper · doi:10.48550/arxiv.1812.11893
Motivated by a number of research questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. Our dual space results clarify the picture of intrinsic transversality, its variants and the only existing sufficient dual condition for subtransversality, and actually unify them. New primal space characterizations of the intrinsic transversality which is originally a dual space condition lead to new understanding of the property in terms of primal space elements for the first time. As a consequence, the obtained analysis allows us to address a number of research questions asked by the two aforementioned researchers about the intrinsic transversality property in the Hilbert space setting.