论文标题
通过自定义交替的乘数方法的非convex半决赛优化的有效方法
An efficient approach for nonconvex semidefinite optimization via customized alternating direction method of multipliers
论文作者
论文摘要
我们研究了一类通用组合图问题，包括最大切割和社区检测，在非convex约束上重新构成了二次目标，并通过乘数的交替方向方法（ADMM）解决。 我们提出了两项重新制定：一种使用向量变量和二进制约束，另一个使用二进制约束，另一个使用载体形式进行了重新重新重新制定以进行简单的子问题。 尽管有非凸的约束，但在轻度假设下，我们证明了ADMM ITERITS在两个配方中的固定点融合。 此外，最近的工作表明，在后一种形式中，当矩阵因子足够宽时，具有很高概率的局部最佳也是全球最佳的。 为了证明算法的可扩展性，我们包括最大切割，社区检测和图像分割基准和模拟示例的结果。
We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers (ADMM). We propose two reformulations: one using vector variables and a binary constraint, and the other further reformulating the Burer-Monteiro form for simpler subproblems. Despite the nonconvex constraint, we prove the ADMM iterates converge to a stationary point in both formulations, under mild assumptions. Additionally, recent work suggests that in this latter form, when the matrix factors are wide enough, local optimum with high probability is also the global optimum. To demonstrate the scalability of our algorithm, we include results for MAX-CUT, community detection, and image segmentation benchmark and simulated examples.
