Year: 2024
Type: preprint
Abstract: Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint selection method, rotational adjusting method (RAM), to minimize the approximation error between the original function and the piecewise linear function with limited number of pieces, applicable to both convex or concave function. RAM rotationally adjusts the location of breakpoints based on its adjacent breakpoints, and the optimal positions would be reached after several iterations. The optimality of the method is proved. Numerical experiments are conducted on the logarithmic function.
Source: arXiv (Cornell University)
Author: Liu, Shaojun
Institution: Nanyang Technological University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ministry of Education, India
OpenAlex ID: W4401306307