The lower bounded inverse optimal value problem on minimum spanning tree under unit $$l_{\infty }$$ l ∞ norm

Binwu Zhang, Xiucui Guan (), Panos M. Pardalos, Hui Wang, Qiao Zhang, Yan Liu and Shuyi Chen
Additional contact information
Binwu Zhang: Hohai University
Xiucui Guan: Southeast University
Panos M. Pardalos: University of Florida
Hui Wang: Southeast University
Qiao Zhang: Southeast University
Yan Liu: Hohai University
Shuyi Chen: Hohai University

Journal of Global Optimization, 2021, vol. 79, issue 3, No 10, 757-777

Abstract: Abstract We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit $$l_{\infty }$$ l ∞ norm. Given an edge weighted connected undirected network $$G=(V,E,\varvec{w})$$ G = ( V , E , w ) , a spanning tree $$T^0$$ T 0 , a lower bound vector $$\varvec{l}$$ l and a value K, we aim to find a new weight vector $$\bar{\varvec{w}}$$ w ¯ respecting the lower bound such that $$T^0$$ T 0 is a minimum spanning tree under the vector $$\bar{\varvec{w}}$$ w ¯ with weight K, and the objective is to minimize the modification cost under unit $$l_{\infty }$$ l ∞ norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop a strongly polynomial time algorithm with running time O(|V||E|). Finally, we give an example to demonstrate the algorithm and present the numerical experiments.

Keywords: Minimum spanning tree; $$l_\infty $$ l ∞ norm; Inverse optimal value problem; Strongly polynomial time algorithm (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-020-00947-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00947-3

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-020-00947-3

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().