We propose a generalized framework for block-structured nonconvex optimization, which can be applied to structured subgraph detection in interdependent networks, such as multi-layer networks, temporal networks, networks of networks, and many others. Specifically, we design an effective, efficient, and parallelizable projection algorithm, namely Graph Block-structured Gradient Projection (GBGP), to optimize a general non-linear function subject to graph-structured constraints. We prove that our algorithm: 1) runs in nearly-linear time on the network size; 2) enjoys a theoretical approximation guarantee. Moreover, we demonstrate how our framework can be applied to two very practical applications and conduct comprehensive experiments to show the effectiveness and efficiency of our proposed algorithm.
翻译：我们提议了一个块状结构非电流优化通用框架,可用于在多层网络、时间网络、网络网络和许多其他网络等相互依存网络中进行结构化子图检测。具体地说,我们设计了一个有效、高效和可平行的预测算法,即“块状结构梯度预测法 ” ( GBGP),以优化受图形结构制约的一般非线性功能。我们证明我们的算法:1)在网络规模上运行的近线时间;2)享有理论近似保证。此外,我们证明我们的框架如何适用于两个非常实用的应用,并进行全面实验,以显示我们提议的算法的有效性和效率。
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