The lower bounded inverse optimal value problem on minimum spanning tree under unit l∞ norm - Zhang, Binwu; Guan, Xiucui; Pardalos, Panos M.; Wang, Hui; Zhang, Qiao; Liu, Yan; Chen, Shuyi (Journal of global optimization, 2021)
We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit l ∞ norm. Given an edge weighted connected undirected network G = ( V , E , w ) , a spanning tree T 0 , a lower bound vector l and a value K , we aim to find a new weight vector w ¯ respecting the lower bound such that T 0 is a minimum spanning tree under the vector w ¯ with weight K , and the objective is to minimize the modification cost under unit 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.