论文标题
用于非对称非负矩阵三因素化的非平滑型非covex问题的固定惯性Bregman近端算法
A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization
论文作者
论文摘要
我们提出了BIBPA，BIBPA是一种块惯性的Bregman近端算法，用于最大程度地减少块相对平滑函数的总和（即相对平滑，每个块）和可分开的非平滑非凸函数。我们证明，BIBPA生成的序列随后在标准假设下会收敛到目标的临界点，并且当额外假定目标函数满足Kurdyka-lojasiewicz（Kł）属性时，全球收敛。当目标满足不平等现象时，我们还提供收敛速度。我们将BIBPA应用于对称非负矩阵三因素化（SymtrinMF）问题，在其中我们提出了SymtrinMF的内核函数，并为BIBPA子问题提供了封闭形式的溶液。
We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We prove that the sequence generated by BIBPA subsequentially converges to critical points of the objective under standard assumptions, and globally converges when the objective function is additionally assumed to satisfy the Kurdyka-Łojasiewicz (KŁ) property. We also provide the convergence rate when the objective satisfies the Łojasiewicz inequality. We apply BIBPA to the symmetric nonnegative matrix tri-factorization (SymTriNMF) problem, where we propose kernel functions for SymTriNMF and provide closed-form solutions for subproblems of BIBPA.
