Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

应用半二次优化于损失函数可以产生对应的正则化器，而这些正则化器通常不具备稀疏诱导能力。为解决这个问题，我们设计了一个能够生成具有闭式近似算子的稀疏诱导能力正则化器的框架。此外，我们使用几个常用的损失函数来明确我们的框架，并产生相应的正则化器，这些正则化器则被采用作为非凸秩代理用于低秩矩阵完成。此外，我们还开发了基于交替方向乘子法的算法。广泛的数值结果表明我们方法在恢复性能和运行时间方面的有效性。

增强低秩矩阵补全的稀疏正则化生成框架