
Journal of Convex Analysis 26 (2019), No. 4, 10891112 Copyright Heldermann Verlag 2019 Shortest Paths along a Sequence of Line Segments in Euclidean Spaces Nguyen Ngoc Hai Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam nnhai@hcmiu.edu.vn Phan Thanh An Institute of Mathematics and Computer Science, University of Sao Paulo, Sao Carlos  SP, Brasil and: Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi, Vietnam thanhan@math.ac.vn Phong Thi Thu Huyen Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi, Vietnam ptthuyen@math.ac.vn We present some analytical and geometric properties of shortest ordered paths joining two given points with respect to a sequence of line segments in a Euclidean space, especially their existence, uniqueness, characteristics, and conditions for concatenation of two shortest ordered paths to be a shortest ordered path. We then focus on straightest paths lying on a sequence of adjacent convex polygons in 2 or 3 dimensional spaces. Keywords: Shortest paths, ordered paths, shortest ordered paths, straightest paths, concatenation of paths. MSC: 65K10, 52B05, 52B55, 51M20. [ Fulltextpdf (240 KB)] for subscribers only. 