TY - JOUR AU - Nhan, Tran Hoai Ngoc AU - Nguyen, Kien Trung AU - Hung, Nguyen Thanh AU - Toan, Nguyen Thanh PY - 2022/12/28/ TI - The Inverse k-Max Combinatorial Optimization Problem JF - Yugoslav Journal of Operations Research; Vol 33 No 2 (2023)DO - 10.2298/YJOR220516037N KW - N2 - Classical combinatorial optimization problem is to find a feasible subset of a ground set in order to optimize an objective function. We address in this article the inverse optimization problem with the k-max function. In other words, we attempt to perturb the weights of elements in the ground set at minimum total cost  to make a predetermined subset optimal in the fashion of the k-max objective with respect to the perturbed weights. We first show that the problem is in general NP-hard. Regarding the case of independent feasible subsets, a combinatorial O(n^2\log n) time algorithm is developed,  where n is the number of elements in E. Special cases with improved complexity are also discussed. UR - https://yujor.fon.bg.ac.rs/index.php/yujor/article/view?path=