反Cheeger割的连续迭代算法
Continuous iterative algorithms for anti-Cheeger cut
AI总结：
本文针对反Cheeger割问题提出一种无需舍入的连续迭代算法（CIA），其子问题具有显式解析解且可在有限步内收敛到局部最优，并能与最大割迭代结合提升解质量，在G-set上实验表明其解质量与启发式方法相当且计算速度更快。
摘要：
作为经典最大割问题的一种合理对应，反Cheeger割具有更均衡的结构，但迄今为止关于它的数值结果报道很少。本文通过充分利用一个等价的连续公式，提出了求解反Cheeger割问题的连续迭代算法（CIA）。该算法完全不需要舍入操作，并具有以下优点：所有子问题都有显式解析解，目标函数值单调更新，且通过适当的次梯度选择，迭代点可在有限步内收敛到局部最优。由于反Cheeger割问题与最大割问题之间的相似性，该算法还可以容易地与最大割迭代相结合，从而跳出局部最优并提高解的质量。通过在G-set上的数值实验，从两个方面充分展示了CIA的性能：一是在解的质量方面，我们发现CIA获得的近似解与多重搜索算子启发式方法得到的解质量相当；二是在计算代价方面，我们表明CIA总是比常用的基于秩二松弛的连续迭代算法运行得更快。
英文摘要：
As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the anti-Cheeger cut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the objective function values are monotonically updated and the iteration points converge to a local optimum in finite steps via an appropriate subgradient selection. It can also be easily combined with the maxcut iterations for breaking out of local optima and improving the solution quality thanks to the similarity between the anti-Cheeger cut problem and the maxcut problem. The performance of CIAs is fully demonstrated through numerical experiments on G-set from two aspects: one is on the solution quality where we find that the approximate solutions obtained by CIAs are of comparable quality to those by the multiple search operator heuristic method; the other is on the computational cost where we show that CIAs always run faster than the often-used continuous iterative algorithm based on the rank-two relaxation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
