Integer and combinatorial optimization
Integer and combinatorial optimization
Computational difficulties of bilevel linear programming
Operations Research
New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
On an instance of the inverse shortest paths problem
Mathematical Programming: Series A and B
Discrete linear bilevel programming problem
Journal of Optimization Theory and Applications
Operations Research
The inverse optimal value problem
Mathematical Programming: Series A and B
On the Global Solution of Linear Programs with Linear Complementarity Constraints
SIAM Journal on Optimization
Heuristic algorithms for the inverse mixed integer linear programming problem
Journal of Global Optimization
Inverse problems of some NP-complete problems
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Operations Research Letters
Cutting plane algorithms for the inverse mixed integer linear programming problem
Operations Research Letters
Inverse conic programming with applications
Operations Research Letters
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This paper presents branch-and-bound algorithms for the partial inverse mixed integer linear programming (PInvMILP) problem, which is to find a minimal perturbation to the objective function of a mixed integer linear program (MILP), measured by some norm, such that there exists an optimal solution to the perturbed MILP that also satisfies an additional set of linear constraints. This is a new extension to the existing inverse optimization models. Under the weighted $$L_1$$ and $$L_\infty $$ norms, the presented algorithms are proved to finitely converge to global optimality. In the presented algorithms, linear programs with complementarity constraints (LPCCs) need to be solved repeatedly as a subroutine, which is analogous to repeatedly solving linear programs for MILPs. Therefore, the computational complexity of the PInvMILP algorithms can be expected to be much worse than that of MILP or LPCC. Computational experiments show that small-sized test instances can be solved within a reasonable time period.