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 show that the cluster points of the sequence generated by BIBPA are critical points of the objective under standard assumptions, and this sequence converges globally when a regularization of the objective function satisfies the Kurdyka-Łojasiewicz (KL) property. We also provide the convergence rate when a regularization of the objective function 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.

我们提出了BIBPA，一种块惯性 Bregman 近端算法，用于最小化块相对平滑函数（即每个块相对平滑）和块可分离非光滑非凸函数的总和。我们表明，在标准假设下，由 BIBPA 生成的序列的聚类点是目标的关键点，并且当目标函数的正则化满足 Kurdyka-Łojasiewicz (KL) 属性时，该序列全局收敛。当目标函数的正则化满足 Łojasiewicz 不等式时，我们还提供了收敛速度。我们将 BIBPA 应用于对称非负矩阵三分解 (SymTriNMF) 问题，我们为 SymTriNMF 提出核函数并为以下子问题提供封闭形式的解决方案比比帕。