Abstract
In this paper, we first discuss a class of inverse dominant problems under weighted l ∞ norm, which is how to change the original weights of elements with bounds in a finite ground set so that a given set becomes a weakly dominant set with respect to a given collection of subsets under the new weights and the largest change of the weights is minimum. This model includes a large class of improvement problems in combinatorial optimization. We propose a Newton-type algorithm for the model. This algorithm can solve the model in strongly polynomial time if the subproblem involved is solvable in strongly polynomial time. In the second part of the paper, we improve the complexity bound for Radzik’s Newton-type method which is designed to solve linear fractional combinatorial optimization problems. As Radzik’s method is closely related to our algorithm, this bound also estimates the complexity of our algorithm.
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Supported by the Hong Kong Universities Grant Council (CERG CITYU 9040883 and 9041091).
Xiaoguang Yang - The author is also grateful for the support by the National Key Research and Development Program of China (Grant No. 2002CB312004) and the National Natural Science Foundation of China (Grant No. 70425004).
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Wang, Q., Yang, X. & Zhang, J. A Class of Inverse Dominant Problems under Weighted l ∞ Norm and an Improved Complexity Bound for Radzik’s Algorithm. J Glob Optim 34, 551–567 (2006). https://doi.org/10.1007/s10898-005-1649-y
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DOI: https://doi.org/10.1007/s10898-005-1649-y