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.

翻译：将半二次优化应用于损失函数可得到相应的正则化器，但这些正则化器通常并非稀疏诱导正则化器（SIR）。为解决此问题，我们设计了一种框架来生成具有闭式邻近算子的SIR。此外，我们使用几种常用损失函数具体化该框架，并生成对应的SIR，随后将其作为非凸秩代理函数用于低秩矩阵补全。进一步地，我们开发了基于交替方向乘子法的算法。大量数值结果表明，我们的方法在恢复性能和运行时间方面均具有有效性。