In this working note, we make some observations about the equivalences between regularized estimating equations, fixed-point problems and variational inequalities. A summary of our findings is given below: (a) A regularized estimating equation is equivalent to a fixed-point problem, specified by the proximal operator of the corresponding penalty; (b) A regularized estimating equation is equivalent to a generalized variational inequality; (c) Both equivalences extend to any estimating equations and any penalty functions. To our knowledge, these observations have never been presented in the literature before. We hope our new findings can lead to further research in both computational and theoretical aspects of regularized estimating equations.

翻译：在本工作说明中,我们对定期估算方程式、固定点问题和差异性不平等之间的等同性提出一些意见,我们的结论摘要如下:(a) 定期估算方程式相当于固定点问题,由相应刑罚的准操作者具体规定;(b) 定期估算方程式相当于普遍差异性不平等;(c) 两种等同都延伸到任何估算方程式和任何处罚功能。据我们所知,这些看法从未在文献中出现过。我们希望我们的新发现能够导致对定期估算方程式的计算和理论方面的进一步研究。