Minimum cost network flow with interval capacities: The worst-case scenario
Prague University of Economics and Business（布拉格经济商业大学）；Charles University（查理大学）；Czech University of Life Sciences Prague（捷克生命科学大学布拉格分校）；University of Salerno（萨莱诺大学）
Miroslav Rada, Milan Hladík, Elif Radová Garajová, Francesco Carrabs, Raffaele Cerulli, Ciriaco D'Ambrosio
We study the problem of determining the worst optimal value and characterizing the corresponding worst-case scenarios in minimum cost network flow problems with interval uncertainty in arc capacities. In this setting, each capacity can take any value within its specified lower and upper bounds. We prove that computing the worst optimal value is a strongly NP-hard problem and remains NP-hard even when restricted to series-parallel graphs. Further, we propose a mixed-integer linear programming formulation that computes the exact worst optimal value, as well as a pseudopolynomial-time algorithm designed for the special case of series-parallel graphs. We also examine the structural properties of the most extremal worst-case scenarios and show that the arcs whose capacities are not fixed at their interval bounds form a forest. This result establishes an upper bound on the number of such arcs, which we show to be tight by constructing a class of instances in which the bound is attained. Finally, we investigate the more-for-less paradox in minimum cost network flow problems with interval capacities, which occurs in instances where increasing the required flow leads to a decrease in the worst-case optimal cost. We provide a general characterization of this phenomenon using augmenting paths and establish a stronger characterization for complete graphs. In addition, we discuss the properties of the cost matrices immune against the paradox and prove that deciding whether a given cost matrix has this property is a strongly co-NP-hard problem.
Stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays
The Sharp Worst-Case Asymptotic Rate of the Barzilai--Borwein Method in $\mathbb R^d$ and Hilbert Spaces
State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
University of Warwick（华威大学）；National University of Singapore（新加坡国立大学）；Macquarie University（麦考瑞大学）；Australian National University（澳大利亚国立大学）；Centre for Quantum Computation and Communication Technology, Australian Research Council（澳大利亚研究委员会量子计算与通信技术中心）
