We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weights. We propose two novel strategies combining Krylov subspace approximations with a greedy scheme and an interior point method employing either the Hessian or its approximation computed via the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS). The paper discusses the computational and modeling aspects of our methodology and illustrates the various optimization problems on networks that can be addressed within the proposed framework. Finally, in the numerical experiments we compare the performances of our algorithms with state-of-the-art techniques on synthetic and real-world networks.

翻译：考虑通过有界修改边权重子集来实现复杂网络鲁棒性的最大增强或减弱问题。我们提出两种新策略，将Krylov子空间近似与贪婪方案相结合，以及采用基于海森矩阵或其通过有限内存Broyden-Fletcher-Goldfarb-Shanno算法（L-BFGS）计算的近似的内点法。本文讨论了该方法的计算与建模方面，并阐述了在该框架下可解决的各种网络优化问题。最后，在数值实验中，我们将算法性能与合成网络及真实网络上的最新技术进行了比较。