Journal of Convex Analysis 26 (2019), No. 4, 1089--1112
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
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
Phong Thi Thu Huyen
Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi, Vietnam
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.
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