基于SIS模型的大型网络最优网络安全投资：算法设计
Optimal Cybersecurity Investments in Large Networks Using SIS Model: Algorithm Design
摘要：
我们研究的问题，最小化（时间）平均安全成本在大型网络/系统，包括许多相互依赖的子系统，其中的状态演变是由一个易感染的易感（SIS）模型捕获。安全成本反映了安全投资、经济损失以及成功攻击后的感染和失败的恢复成本。我们表明，由此产生的优化问题是非凸的，并提出了一套算法-两个凸松弛的基础上，和其他两个找到一个局部极小值，减少梯度法和顺序凸规划的基础上。此外，我们提供了一个充分条件下，凸松弛是准确的，因此，他们的解决方案与原问题相吻合。数值结果验证了我们的分析结果，并证明所提出的算法的有效性。
英文摘要：
We study the problem of minimizing the (time) average security costs in large networks/systems comprising many interdependent subsystems, where the state evolution is captured by a susceptible-infected-susceptible (SIS) model. The security costs reflect security investments, economic losses and recovery costs from infections and failures following successful attacks. We show that the resulting optimization problem is nonconvex and propose a suite of algorithms - two based on a convex relaxation, and the other two for finding a local minimizer, based on a reduced gradient method and sequential convex programming. Also, we provide a sufficient condition under which the convex relaxations are exact and, hence, their solution coincides with that of the original problem. Numerical results are provided to validate our analytical results and to demonstrate the effectiveness of the proposed algorithms.
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